Keywords: Exp-function method; solitary wave solutions; modified Camassa-Holm

Size: px
Start display at page:

Download "Keywords: Exp-function method; solitary wave solutions; modified Camassa-Holm"

Transcription

1 International Journal of Modern Mathematical Sciences, 2012, 4(3): International Journal of Modern Mathematical Sciences Journal homepage: ISSN: X Florida, USA Article Exp-function Method for Simplified Modified Camassa Holm Equation Amna Irshad, Muhammad Usman and Syed Tauseef Mohyud-Din* Department of Mathematics, Faculty of Sciences, HITEC University, Taxila Cantt Pakistan * Author to whom correspondence should be addressed; syedtauseefs@hotmail.com Article history: Received 17 September 2012, Received in revised form 17 December 2012, Accepted 20 December 2012, Published 21 December Abstract: Explicit solitary wave solutions of modified Camassa-Holm equation are constructed by using Exp-function method. Numerical results are true reflection of the efficiency and reliability of the proposed algorithm. Keywords: Exp-function method; solitary wave solutions; modified Camassa-Holm equations, nonlinear problems. Mathematics Subject Classification: 35Q79 1. Introduction Partial differential equations [1-32] arise very frequently in physical models. The thorough study of literature reveals [1-32] that most of the physical phenomenon is best modeled by nonlinear differential equations. Inspired and motivated by the ongoing research in this area, we apply a relatively new technique which is called the exp-function method [1, 3-6, 16-27] to find solitary wave solutions of nonlinear modified Camassa-Holm equation. which arise frequently in number of scientific models including fluid mechanics, astrophysics, solid state physics, plasma physics, chemical kinematics, chemical physics, optical fiber and geochemistry, see [16, 29-32] and the references therein. It is to be highlighted that exp-function method has been applied on a wide range of nonlinear diversified physical problems including, high-dimensional nonlinear evolution equation, combined KdV and mkdv, Hybrid-Lattice system and discrete mkdv lattice [1, 3-6, 16-27].

2 Camassa and Holm Equations Camassa and Holm [29] derived a completely integrable wave equation (CH equation) for water waves (1.1) by retaining two terms that are usually neglected in the small amplitude, shallow water limit. Tian and Song [30] investigated a modified Camassa Holm equation (MCH equation) (1.2) and obtained new peaked solitary wave solutions. In addition, Boyd [31] investigated that if the solitary wave varies slowly with then the two extra terms on the right-hand side of (1.1) will be small and the soliton is given to lowest order by the solutions of (1.3) In view of (1.3), Wazwaz [32] investigated a modified form of Camassa -Holm equation, which is simplified from MCH equation and given by (1.4) In this paper, we only consider, (1.5) and for simplicity we call (1.5) simplified MCH equation. 3. Exp-function Method [1, 3-6, 16-27] Consider the following general partial differential equation: ) = 0. (2.1) We first unite the independent variables x and t into one wave variable (2.2) to an ordinary differential equation, ) (2.2) leading The Exp-function method is based on the assumption that traveling wave solutions can be expressed in the following form [30]: ). (2.3) c, d, p, and q are positive integers which are unknown to be further determined, and and are unknown constants. To determine the values of c and p, we balance the linear term of highest order in (2.2) with the highest-order nonlinear term. Similarly to determine the values of d and q, we balance the linear term of lowest order in (2.2) with the lowest-order nonlinear term.

3 Numerical Applications In this section we apply Exp-function Method for solving simplified MCH equation. (3.1) Introducing a transformation as equations Integrating Eq. (3.2) with respect to once, we get ), we can convert (3.1) into ordinary differential (3.2) (3.3) The solution of (3.3) can be expressed in the form, (2.3) as To determine the values of can d p, we balance the highest order linear term of (3.3) with the highest order nonlinear term. Therefore, we have and [ ) ] (3.4) [ ) ] (3.5) are coefficients for simplicity; by balancing the highest order of the exp-function, we obtain, (3.6) Which is turns gives (3.7) To determine the values of d and q, we balance the lowest order linear term of (3.2) with the lowest order nonlinear term. Therefore and [ ) ] (3.8) [ ) ] (3.9) are determined coefficients only for simplicity; Now balancing the lowest order of the expfunction, we obtain (3.10)

4 149 which is turns gives (3.11) Case 4.1.1: p = c = 1, and q = d = 1. Equation (2.3) reduces to (3.12) Substituting (3.12) into (3.3), we have ) (3.13) ), Equating the coefficients of ) to be zero, we obtain { } (3.14) We have the following set of Solution First set: Second set: (3.15) Third set: (3.16) (3.17) Now, substituting (3.15) into (3.12), we get the generalized solitary wave solution (3.18)

5 150 next, substituting (3.16) into (3.12), we get the following generalized solitary wave solution (3.19) finally, substituting (3.17) into (3.12), we get the resulting solution (3.20) are real numbers. Case 3.1.2:, and. Equation (2.3) reduces to (3.21) In (3.21), there are some parameters, we set [ simplified as follows ] for simplicity and the trial function is (3.22) substituting (3.22) into (3.3) we have ) (3.23) ), Equating the coefficients of ) to be zero, we obtain { } (3.24) We have the following set of Solution First set:

6 151 (3.25) Second set: (3.26) Third set: (3.27) Now, substituting (3.25) into (3.21), we get the generalized solitary wave solution (3.28) next, substituting (3.26) into (3.21), we get the following generalized solitary wave solution (3.29) finally, substituting (3.27) into (3.21), we get the resulting solution (3.30) Case 3.1.3:, and Equation (2.3) reduces to (3.31)

7 In (3.31), there are some parameters, we set trial function is simplified as follows for simplicity and the 152 (3.32) First set: Proceeding as before, we obtain the solution sets Second set:. (3.33) Third set: (3.34) Now, substituting (3.33) into (3.31), we get the generalized solitary wave solution (3.35) (3.36) next, substituting (3.34) into (3.31), we get the following generalized solitary wave solution (3.37) finally, substituting (3.35) into (3.31), we get the resulting solution

8 153 (3.38) 4. Conclusions In this paper, we applied exp-function method to obtain generalized solitary solutions of the modified Camassa-Holm equation. Numerical results re-confirm the efficiency and reliability of the proposed Exp-function method. References [1] M. A. Abdou, A. A. Soliman and S. T. Basyony, New application of exp-function method for improved Boussinesq equation. Phys. Lett. A, 369 (2007): [2] J. M. Burgers, A mathematical model illustrating the theory of turbulence, Adv. Appl. Mech. 1(1948): [3] S. A. El-Wakil, M. A. Madkour and M. A. Abdou, Application of exp-function method for nonlinear evolution equations with variable co-efficient, Phys. Lett. A, 369 (2007): [4] J. H. He, An elementary introduction of recently developed asymptotic methods and nanomechanics in textile engineering, Int. J. Mod. Phys. B 22 (21) (2008): [5] J. H. He and X. H. Wu, exp-function method for nonlinear wave equations, Chaos, Solitons & Fractals, 30(3)(2006): [6] J. H. He and M. A. Abdou, New periodic solutions for nonlinear evolution equation using expmethod, Chaos, Solitons & Fractals, 34 (2007): [7] W. Hereman and A. Nuseir, Symbolic methods to construct exact solutions of nonlinear partial differential equations, Math. Comput. Simulation, 43(1997): [8] R. Hirota, The Direct Method in Soliton Theory, Cambridge University Press, Cambridge, [9] R.M. Miura, The Korteweg de-vries equation: a survey of results, SIAM Rev., 18(1976): [10] W. X. Ma, Complexiton solutions to the Korteweg-de Vries equation, Phys. Lett. A, 301 (2002):

9 154 [11] W. X. Ma and B. Fuchssteiner, Explicit and exact solutions of Kolmogorov-PetrovskII-Piskunov equation, Int. J. Nonlin. Mech. 31 (3) (1996): [12] W. X. Ma and Y. You, Solving the Korteweg-de Vries equation by its bilinear form: Wronskian solutions, Transactions of the American Mathematical Society, 357(2004): [13] W. X. Ma and Y. You, Rational solutions of the Toda lattice equation in Casoratian form, Chaos, Solitons & Fractals, 22 (2004): [14] W. X. Ma, H. Y. Wu and J. S. He, Partial differential equations possessing Frobenius integrable decompositions, Phys. Lett. A, 364 (2007): [15] F. Tascan, A. Bekir and M. Kopran, Traveling wave solutions of nonlinear evolution equation by using the first-integral method, Commun. Nonlin. Sci. Num. Sim. (2008), doi /j.cnsns [16] S. T. Mohyud-Din, M. A. Noor and K. I. Noor, Some relatively new techniques for nonlinear problems, Mathematical Problems in Engineering, Hindawi, 2009 (2009); Article ID , 25 pages, doi: /2009/ [17] S. T. Mohyud-Din, Solution of nonlinear differential equations by exp-function method, World Applied Sciences Journal, 7 (2009): [18] M. A. Noor, S. T. Mohyud-Din and A. Waheed, Exp-function method for solving Kuramoto- Sivashinsky and Boussinesq equations, J. Appl. Math. Computg. (2008), DOI: /s y. [19] S. T. Mohyud-Din, M. A. Noor and A. Waheed, Exp-function method for generalized travelling solutions of Calogero-Degasperis-Fokas equation, Zeitschrift für Naturforschung A- A Journal of Physical Sciences, 65a (2010): [20] A. M. Wazwaz, The extended tanh method for Zakharov-Kuznetsov equation (ZK), the modified ZK equation and its generalized forms, Commun. Nonlin. Sci. Num. Sim. 13(2008): [21] S. T. Mohyud-Din, M. A. Noor and A. Waheed, Exp-function method for generalized travelling solutions of good Boussinesq equations, Journal of Applied Mathematics and Computing Springer, 29 (2008), 81-94, DOI /s [22] X. H. Wu and J. H. He, Solitary solutions, periodic solutions and compacton like solutions using the exp-function method, Comput. Math. Appl. 54 (2007): [23] E. Yusufoglu, New solitonary solutions for the MBBN equations using exp-function method, Phys. Lett. A. 372 (2008): [24] X. W. Zhou, Y. X. Wen and J. H. He, Exp-function method to solve the nonlinear dispersive k(m, n) equations, Int. J. Nonlin. Sci. Num. Sim. 9(3) (2008):

10 155 [25] S. Zhang, Application of exp-function method to high-dimensional nonlinear evolution equation, Chaos Solitons &Fractals. 365 (2007): [26] S. D. Zhu, Exp-function method for the Hybrid-Lattice system, Inter. J. Nonlin. Sci. Numer. Sim. 8(2007): [27] S. D. Zhu, Exp-function method for the discrete mkdv lattice, Inter. J. Nonlin. Sci. Numer. Sim. 8(2007): [28] A. M. Wazwaz, Burger hierarchy in ) dimension: Multiple Kink Solutions and Multiple Singular Solutions, Inter. J. Nonlin. Sci. 10(2010): [29] R. Camassa, D. Holm, An integrable shallow water equation with peaked solitons, Phys. Rev. Lett. 71(11) (1993): [30] L. Tian, X. Song, New peaked solitary wave solutions of the generalized Camassa Holm equation, Chaos Solitons & Fractals. 19 (2004): [31] J. P. Boyd, Peakons and cashoidal waves: traveling wave solutions of the Camassa Holm equation, Appl. Math. Comput. 81 (2 3) (1997): [32] A. Wazwaz, New compact and noncompact solutions for two variants of a modified Camassa Holm equation, Appl. Math. Comput. 163 (3) (2005):

EXP-FUNCTION METHOD FOR SOLVING HIGHER-ORDER BOUNDARY VALUE PROBLEMS

EXP-FUNCTION METHOD FOR SOLVING HIGHER-ORDER BOUNDARY VALUE PROBLEMS Bulletin of the Institute of Mathematics Academia Sinica (New Series) Vol. 4 (2009), No. 2, pp. 219-234 EXP-FUNCTION METHOD FOR SOLVING HIGHER-ORDER BOUNDARY VALUE PROBLEMS BY SYED TAUSEEF MOHYUD-DIN,

More information

VARIATION OF PARAMETERS METHOD FOR SOLVING SIXTH-ORDER BOUNDARY VALUE PROBLEMS

VARIATION OF PARAMETERS METHOD FOR SOLVING SIXTH-ORDER BOUNDARY VALUE PROBLEMS Commun. Korean Math. Soc. 24 (29), No. 4, pp. 65 615 DOI 1.4134/CKMS.29.24.4.65 VARIATION OF PARAMETERS METHOD FOR SOLVING SIXTH-ORDER BOUNDARY VALUE PROBLEMS Syed Tauseef Mohyud-Din, Muhammad Aslam Noor,

More information

SOLUTION OF TROESCH S PROBLEM USING HE S POLYNOMIALS

SOLUTION OF TROESCH S PROBLEM USING HE S POLYNOMIALS REVISTA DE LA UNIÓN MATEMÁTICA ARGENTINA Volumen 52, Número 1, 2011, Páginas 143 148 SOLUTION OF TROESCH S PROBLEM USING HE S POLYNOMIALS SYED TAUSEEF MOHYUD-DIN Abstract. In this paper, we apply He s

More information

Modified Simple Equation Method and its Applications for some Nonlinear Evolution Equations in Mathematical Physics

Modified Simple Equation Method and its Applications for some Nonlinear Evolution Equations in Mathematical Physics Modified Simple Equation Method and its Applications for some Nonlinear Evolution Equations in Mathematical Physics Elsayed M. E. Zayed Mathematics department, Faculty of Science Zagazig University, Zagazig,

More information

Multiple-Soliton Solutions for Extended Shallow Water Wave Equations

Multiple-Soliton Solutions for Extended Shallow Water Wave Equations Studies in Mathematical Sciences Vol. 1, No. 1, 2010, pp. 21-29 www.cscanada.org ISSN 1923-8444 [Print] ISSN 1923-8452 [Online] www.cscanada.net Multiple-Soliton Solutions for Extended Shallow Water Wave

More information

New Approach of ( Ǵ/G ) Expansion Method. Applications to KdV Equation

New Approach of ( Ǵ/G ) Expansion Method. Applications to KdV Equation Journal of Mathematics Research; Vol. 6, No. ; ISSN 96-9795 E-ISSN 96-989 Published by Canadian Center of Science and Education New Approach of Ǵ/G Expansion Method. Applications to KdV Equation Mohammad

More information

SOLITARY WAVE SOLUTIONS FOR SOME NON-LINEAR PARTIAL DIFFERENTIAL EQUATIONS USING SINE-COSINE METHOD

SOLITARY WAVE SOLUTIONS FOR SOME NON-LINEAR PARTIAL DIFFERENTIAL EQUATIONS USING SINE-COSINE METHOD www.arpapress.com/volumes/vol17issue3/ijrras_17_3_12.pdf SOLITARY WAVE SOLUTIONS FOR SOME NON-LINEAR PARTIAL DIFFERENTIAL EQUATIONS USING SINE-COSINE METHOD Yusur Suhail Ali Computer Science Department,

More information

Exact Travelling Wave Solutions of the Coupled Klein-Gordon Equation by the Infinite Series Method

Exact Travelling Wave Solutions of the Coupled Klein-Gordon Equation by the Infinite Series Method Available at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 93-9466 Vol. 6, Issue (June 0) pp. 3 3 (Previously, Vol. 6, Issue, pp. 964 97) Applications and Applied Mathematics: An International Journal (AAM)

More information

Exact Solutions of the Generalized- Zakharov (GZ) Equation by the Infinite Series Method

Exact Solutions of the Generalized- Zakharov (GZ) Equation by the Infinite Series Method Available at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 193-9466 Vol. 05, Issue (December 010), pp. 61 68 (Previously, Vol. 05, Issue 10, pp. 1718 175) Applications and Applied Mathematics: An International

More information

New Exact Travelling Wave Solutions for Regularized Long-wave, Phi-Four and Drinfeld-Sokolov Equations

New Exact Travelling Wave Solutions for Regularized Long-wave, Phi-Four and Drinfeld-Sokolov Equations ISSN 1749-3889 print), 1749-3897 online) International Journal of Nonlinear Science Vol.008) No.1,pp.4-5 New Exact Travelling Wave Solutions for Regularized Long-wave, Phi-Four and Drinfeld-Sokolov Euations

More information

2. The generalized Benjamin- Bona-Mahony (BBM) equation with variable coefficients [30]

2. The generalized Benjamin- Bona-Mahony (BBM) equation with variable coefficients [30] ISSN 1749-3889 (print), 1749-3897 (online) International Journal of Nonlinear Science Vol.12(2011) No.1,pp.95-99 The Modified Sine-Cosine Method and Its Applications to the Generalized K(n,n) and BBM Equations

More information

The General Form of Linearized Exact Solution for the KdV Equation by the Simplest Equation Method

The General Form of Linearized Exact Solution for the KdV Equation by the Simplest Equation Method Applied and Computational Mathematics 015; 4(5): 335-341 Published online August 16 015 (http://www.sciencepublishinggroup.com/j/acm) doi: 10.11648/j.acm.0150405.11 ISSN: 38-5605 (Print); ISSN: 38-5613

More information

Travelling Wave Solutions for the Gilson-Pickering Equation by Using the Simplified G /G-expansion Method

Travelling Wave Solutions for the Gilson-Pickering Equation by Using the Simplified G /G-expansion Method ISSN 1749-3889 (print, 1749-3897 (online International Journal of Nonlinear Science Vol8(009 No3,pp368-373 Travelling Wave Solutions for the ilson-pickering Equation by Using the Simplified /-expansion

More information

Homotopy Analysis Transform Method for Time-fractional Schrödinger Equations

Homotopy Analysis Transform Method for Time-fractional Schrödinger Equations International Journal of Modern Mathematical Sciences, 2013, 7(1): 26-40 International Journal of Modern Mathematical Sciences Journal homepage:wwwmodernscientificpresscom/journals/ijmmsaspx ISSN:2166-286X

More information

New Iterative Method for Time-Fractional Schrödinger Equations

New Iterative Method for Time-Fractional Schrödinger Equations ISSN 1 746-7233, England, UK World Journal of Modelling and Simulation Vol. 9 2013) No. 2, pp. 89-95 New Iterative Method for Time-Fractional Schrödinger Equations Ambreen Bibi 1, Abid Kamran 2, Umer Hayat

More information

International Journal of Modern Mathematical Sciences, 2012, 3(2): International Journal of Modern Mathematical Sciences

International Journal of Modern Mathematical Sciences, 2012, 3(2): International Journal of Modern Mathematical Sciences Article International Journal of Modern Mathematical Sciences 2012 3(2): 63-76 International Journal of Modern Mathematical Sciences Journal homepage:wwwmodernscientificpresscom/journals/ijmmsaspx On Goursat

More information

HOMOTOPY ANALYSIS METHOD FOR SOLVING KDV EQUATIONS

HOMOTOPY ANALYSIS METHOD FOR SOLVING KDV EQUATIONS Surveys in Mathematics and its Applications ISSN 1842-6298 (electronic), 1843-7265 (print) Volume 5 (21), 89 98 HOMOTOPY ANALYSIS METHOD FOR SOLVING KDV EQUATIONS Hossein Jafari and M. A. Firoozjaee Abstract.

More information

International Journal of Modern Theoretical Physics, 2012, 1(1): International Journal of Modern Theoretical Physics

International Journal of Modern Theoretical Physics, 2012, 1(1): International Journal of Modern Theoretical Physics International Journal of Modern Theoretical Physics, 2012, 1(1): 13-22 International Journal of Modern Theoretical Physics Journal homepage:www.modernscientificpress.com/journals/ijmtp.aspx ISSN: 2169-7426

More information

Traveling wave solutions of new coupled Konno-Oono equation

Traveling wave solutions of new coupled Konno-Oono equation NTMSCI 4, No. 2, 296-303 (2016) 296 New Trends in Mathematical Sciences http://dx.doi.org/10.20852/ntmsci.2016218536 Traveling wave solutions of new coupled Konno-Oono equation Md. Abul Bashar, Gobinda

More information

Exact Solutions for the Nonlinear (2+1)-Dimensional Davey-Stewartson Equation Using the Generalized ( G. )-Expansion Method

Exact Solutions for the Nonlinear (2+1)-Dimensional Davey-Stewartson Equation Using the Generalized ( G. )-Expansion Method Journal of Mathematics Research; Vol. 6, No. ; 04 ISSN 96-9795 E-ISSN 96-9809 Published by Canadian Center of Science and Education Exact Solutions for the Nonlinear +-Dimensional Davey-Stewartson Equation

More information

Research Article New Exact Solutions for the 2 1 -Dimensional Broer-Kaup-Kupershmidt Equations

Research Article New Exact Solutions for the 2 1 -Dimensional Broer-Kaup-Kupershmidt Equations Hindawi Publishing Corporation Abstract and Applied Analysis Volume 00, Article ID 549, 9 pages doi:0.55/00/549 Research Article New Exact Solutions for the -Dimensional Broer-Kaup-Kupershmidt Equations

More information

Periodic, hyperbolic and rational function solutions of nonlinear wave equations

Periodic, hyperbolic and rational function solutions of nonlinear wave equations Appl Math Inf Sci Lett 1, No 3, 97-101 (013 97 Applied Mathematics & Information Sciences Letters An International Journal http://dxdoiorg/101785/amisl/010307 Periodic, hyperbolic and rational function

More information

A NEW VARIABLE-COEFFICIENT BERNOULLI EQUATION-BASED SUB-EQUATION METHOD FOR SOLVING NONLINEAR DIFFERENTIAL EQUATIONS

A NEW VARIABLE-COEFFICIENT BERNOULLI EQUATION-BASED SUB-EQUATION METHOD FOR SOLVING NONLINEAR DIFFERENTIAL EQUATIONS U.P.B. Sci. Bull., Series A, Vol. 76, Iss., 014 ISSN 1-707 A NEW VARIABLE-COEFFICIENT BERNOULLI EQUATION-BASED SUB-EQUATION METHOD FOR SOLVING NONLINEAR DIFFERENTIAL EQUATIONS Bin Zheng 1 In this paper,

More information

SOLUTIONS OF FRACTIONAL DIFFUSION EQUATIONS BY VARIATION OF PARAMETERS METHOD

SOLUTIONS OF FRACTIONAL DIFFUSION EQUATIONS BY VARIATION OF PARAMETERS METHOD THERMAL SCIENCE, Year 15, Vol. 19, Suppl. 1, pp. S69-S75 S69 SOLUTIONS OF FRACTIONAL DIFFUSION EQUATIONS BY VARIATION OF PARAMETERS METHOD by Syed Tauseef MOHYUD-DIN a, Naveed AHMED a, Asif WAHEED c, Muhammad

More information

Application of the trial equation method for solving some nonlinear evolution equations arising in mathematical physics

Application of the trial equation method for solving some nonlinear evolution equations arising in mathematical physics PRMN c Indian cademy of Sciences Vol. 77, No. 6 journal of December 011 physics pp. 103 109 pplication of the trial equation method for solving some nonlinear evolution equations arising in mathematical

More information

PRAMANA c Indian Academy of Sciences Vol. 83, No. 3 journal of September 2014 physics pp

PRAMANA c Indian Academy of Sciences Vol. 83, No. 3 journal of September 2014 physics pp PRAMANA c Indian Academy of Sciences Vol. 83, No. 3 journal of September 204 physics pp. 37 329 Exact travelling wave solutions of the (3+)-dimensional mkdv-zk equation and the (+)-dimensional compound

More information

An Alternative Approach to Differential-Difference Equations Using the Variational Iteration Method

An Alternative Approach to Differential-Difference Equations Using the Variational Iteration Method An Alternative Approach to Differential-Difference Equations Using the Variational Iteration Method Naeem Faraz a, Yasir Khan a, and Francis Austin b a Modern Textile Institute, Donghua University, 1882

More information

A remark on a variable-coefficient Bernoulli equation based on auxiliary -equation method for nonlinear physical systems

A remark on a variable-coefficient Bernoulli equation based on auxiliary -equation method for nonlinear physical systems A remark on a variable-coefficient Bernoulli equation based on auxiliary -equation method for nonlinear physical systems Zehra Pınar a Turgut Öziş b a Namık Kemal University, Faculty of Arts and Science,

More information

Bifurcations of Traveling Wave Solutions for a Generalized Camassa-Holm Equation

Bifurcations of Traveling Wave Solutions for a Generalized Camassa-Holm Equation Computational and Applied Mathematics Journal 2017; 3(6): 52-59 http://www.aascit.org/journal/camj ISSN: 2381-1218 (Print); ISSN: 2381-1226 (Online) Bifurcations of Traveling Wave Solutions for a Generalized

More information

The (G'/G) - Expansion Method for Finding Traveling Wave Solutions of Some Nonlinear Pdes in Mathematical Physics

The (G'/G) - Expansion Method for Finding Traveling Wave Solutions of Some Nonlinear Pdes in Mathematical Physics Vol.3, Issue., Jan-Feb. 3 pp-369-376 ISSN: 49-6645 The ('/) - Expansion Method for Finding Traveling Wave Solutions of Some Nonlinear Pdes in Mathematical Physics J.F.Alzaidy Mathematics Department, Faculty

More information

Improved (G /G)- expansion method for constructing exact traveling wave solutions for a nonlinear PDE of nanobiosciences

Improved (G /G)- expansion method for constructing exact traveling wave solutions for a nonlinear PDE of nanobiosciences Vol 8(5), pp 54-546, 5 ugust, 3 DOI 5897/SRE3555 ISSN 99-48 3 cademic Journals http://wwwacademicjournalsorg/sre Scientific Research and Essays Full Length Research Paper Improved (G /G)- expansion method

More information

Integral Bifurcation Method and Its Application for Solving the Modified Equal Width Wave Equation and Its Variants

Integral Bifurcation Method and Its Application for Solving the Modified Equal Width Wave Equation and Its Variants Rostock. Math. Kolloq. 62, 87 106 (2007) Subject Classification (AMS) 35Q51, 35Q58, 37K50 Weiguo Rui, Shaolong Xie, Yao Long, Bin He Integral Bifurcation Method Its Application for Solving the Modified

More information

A note on the G /G - expansion method

A note on the G /G - expansion method A note on the G /G - expansion method Nikolai A. Kudryashov Department of Applied Mathematics, National Research Nuclear University MEPHI, Kashirskoe Shosse, 115409 Moscow, Russian Federation Abstract

More information

Numerical Simulation of the Generalized Hirota-Satsuma Coupled KdV Equations by Variational Iteration Method

Numerical Simulation of the Generalized Hirota-Satsuma Coupled KdV Equations by Variational Iteration Method ISSN 1749-3889 (print), 1749-3897 (online) International Journal of Nonlinear Science Vol.7(29) No.1,pp.67-74 Numerical Simulation of the Generalized Hirota-Satsuma Coupled KdV Equations by Variational

More information

A NEW APPROACH FOR SOLITON SOLUTIONS OF RLW EQUATION AND (1+2)-DIMENSIONAL NONLINEAR SCHRÖDINGER S EQUATION

A NEW APPROACH FOR SOLITON SOLUTIONS OF RLW EQUATION AND (1+2)-DIMENSIONAL NONLINEAR SCHRÖDINGER S EQUATION A NEW APPROACH FOR SOLITON SOLUTIONS OF RLW EQUATION AND (+2-DIMENSIONAL NONLINEAR SCHRÖDINGER S EQUATION ALI FILIZ ABDULLAH SONMEZOGLU MEHMET EKICI and DURGUN DURAN Communicated by Horia Cornean In this

More information

EXACT BREATHER-TYPE SOLUTIONS AND RESONANCE-TYPE SOLUTIONS OF THE (2+1)-DIMENSIONAL POTENTIAL BURGERS SYSTEM

EXACT BREATHER-TYPE SOLUTIONS AND RESONANCE-TYPE SOLUTIONS OF THE (2+1)-DIMENSIONAL POTENTIAL BURGERS SYSTEM EXACT BREATHER-TYPE SOLUTIONS AND RESONANCE-TYPE SOLUTIONS OF THE (+)-DIMENSIONAL POTENTIAL BURGERS SYSTEM YEQIONG SHI College of Science Guangxi University of Science Technology Liuzhou 545006 China E-mail:

More information

Exp-function Method for Fractional Differential Equations

Exp-function Method for Fractional Differential Equations From the SelectedWorks of Ji-Huan He 2013 Exp-function Method for Fractional Differential Equations Ji-Huan He Available at: https://works.bepress.com/ji_huan_he/73/ Citation Information: He JH. Exp-function

More information

An Analytic Study of the (2 + 1)-Dimensional Potential Kadomtsev-Petviashvili Equation

An Analytic Study of the (2 + 1)-Dimensional Potential Kadomtsev-Petviashvili Equation Adv. Theor. Appl. Mech., Vol. 3, 21, no. 11, 513-52 An Analytic Study of the (2 + 1)-Dimensional Potential Kadomtsev-Petviashvili Equation B. Batiha and K. Batiha Department of Mathematics, Faculty of

More information

The Modified Variational Iteration Method for Solving Linear and Nonlinear Ordinary Differential Equations

The Modified Variational Iteration Method for Solving Linear and Nonlinear Ordinary Differential Equations Australian Journal of Basic and Applied Sciences, 5(10): 406-416, 2011 ISSN 1991-8178 The Modified Variational Iteration Method for Solving Linear and Nonlinear Ordinary Differential Equations 1 M.A. Fariborzi

More information

Multi-Soliton Solutions to Nonlinear Hirota-Ramani Equation

Multi-Soliton Solutions to Nonlinear Hirota-Ramani Equation Appl. Math. Inf. Sci. 11, No. 3, 723-727 (2017) 723 Applied Mathematics & Information Sciences An International Journal http://dx.doi.org/10.18576/amis/110311 Multi-Soliton Solutions to Nonlinear Hirota-Ramani

More information

New approach for tanh and extended-tanh methods with applications on Hirota-Satsuma equations

New approach for tanh and extended-tanh methods with applications on Hirota-Satsuma equations Volume 28, N. 1, pp. 1 14, 2009 Copyright 2009 SBMAC ISSN 0101-8205 www.scielo.br/cam New approach for tanh and extended-tanh methods with applications on Hirota-Satsuma equations HASSAN A. ZEDAN Mathematics

More information

SOLITON SOLUTIONS OF SHALLOW WATER WAVE EQUATIONS BY MEANS OF G /G EXPANSION METHOD

SOLITON SOLUTIONS OF SHALLOW WATER WAVE EQUATIONS BY MEANS OF G /G EXPANSION METHOD Journal of Applied Analysis and Computation Website:http://jaac-online.com/ Volume 4, Number 3, August 014 pp. 1 9 SOLITON SOLUTIONS OF SHALLOW WATER WAVE EQUATIONS BY MEANS OF G /G EXPANSION METHOD Marwan

More information

SolitaryWaveSolutionsfortheGeneralizedZakharovKuznetsovBenjaminBonaMahonyNonlinearEvolutionEquation

SolitaryWaveSolutionsfortheGeneralizedZakharovKuznetsovBenjaminBonaMahonyNonlinearEvolutionEquation Global Journal of Science Frontier Research: A Physics Space Science Volume 16 Issue 4 Version 1.0 Year 2016 Type : Double Blind Peer Reviewed International Research Journal Publisher: Global Journals

More information

Traveling Wave Solutions of the RLW-Burgers Equation and Potential Kdv Equation by Using the - Expansion Method

Traveling Wave Solutions of the RLW-Burgers Equation and Potential Kdv Equation by Using the - Expansion Method Çankaya Üniversitesi Fen-Edebiyat Fakültesi, Journal of Arts and Sciences Sayı: 12 / Aralık 2009 Traveling Wave Solutions of the RLW-Burgers Equation and Potential Kdv Equation by Using the - Expansion

More information

The Solitary Wave Solutions of Zoomeron Equation

The Solitary Wave Solutions of Zoomeron Equation Applied Mathematical Sciences, Vol. 5, 011, no. 59, 943-949 The Solitary Wave Solutions of Zoomeron Equation Reza Abazari Deparment of Mathematics, Ardabil Branch Islamic Azad University, Ardabil, Iran

More information

Compacton Solutions and Peakon Solutions for a Coupled Nonlinear Wave Equation

Compacton Solutions and Peakon Solutions for a Coupled Nonlinear Wave Equation ISSN 1749-3889 (print), 1749-3897 (online) International Journal of Nonlinear Science Vol 4(007) No1,pp31-36 Compacton Solutions Peakon Solutions for a Coupled Nonlinear Wave Equation Dianchen Lu, Guangjuan

More information

The Modified (G /G)-Expansion Method for Nonlinear Evolution Equations

The Modified (G /G)-Expansion Method for Nonlinear Evolution Equations The Modified ( /-Expansion Method for Nonlinear Evolution Equations Sheng Zhang, Ying-Na Sun, Jin-Mei Ba, and Ling Dong Department of Mathematics, Bohai University, Jinzhou 11000, P. R. China Reprint requests

More information

Research Article Two Different Classes of Wronskian Conditions to a (3 + 1)-Dimensional Generalized Shallow Water Equation

Research Article Two Different Classes of Wronskian Conditions to a (3 + 1)-Dimensional Generalized Shallow Water Equation International Scholarly Research Network ISRN Mathematical Analysis Volume 2012 Article ID 384906 10 pages doi:10.5402/2012/384906 Research Article Two Different Classes of Wronskian Conditions to a 3

More information

New Exact Solutions of the Modified Benjamin-Bona-Mahony Equation Yun-jie YANG and Li YAO

New Exact Solutions of the Modified Benjamin-Bona-Mahony Equation Yun-jie YANG and Li YAO 06 International Conference on Artificial Intelligence and Computer Science (AICS 06) ISBN: 978--60595-4-0 New Exact Solutions of the Modified Benamin-Bona-Mahony Equation Yun-ie YANG and Li YAO Department

More information

The Traveling Wave Solutions for Nonlinear Partial Differential Equations Using the ( G. )-expansion Method

The Traveling Wave Solutions for Nonlinear Partial Differential Equations Using the ( G. )-expansion Method ISSN 1749-3889 (print), 1749-3897 (online) International Journal of Nonlinear Science Vol.8(009) No.4,pp.435-447 The Traveling Wave Solutions for Nonlinear Partial Differential Equations Using the ( )-expansion

More information

An efficient algorithm for computation of solitary wave solutions to nonlinear differential equations

An efficient algorithm for computation of solitary wave solutions to nonlinear differential equations Pramana J. Phys. 017 89:45 DOI 10.1007/s1043-017-1447-3 Indian Academy of Sciences An efficient algorithm for computation of solitary wave solutions to nonlinear differential equations KAMRAN AYUB 1, M

More information

The cosine-function method and the modified extended tanh method. to generalized Zakharov system

The cosine-function method and the modified extended tanh method. to generalized Zakharov system Mathematica Aeterna, Vol. 2, 2012, no. 4, 287-295 The cosine-function method and the modified extended tanh method to generalized Zakharov system Nasir Taghizadeh Department of Mathematics, Faculty of

More information

EXACT SOLUTION TO TIME FRACTIONAL FIFTH-ORDER KORTEWEG-DE VRIES EQUATION BY USING (G /G)-EXPANSION METHOD. A. Neamaty, B. Agheli, R.

EXACT SOLUTION TO TIME FRACTIONAL FIFTH-ORDER KORTEWEG-DE VRIES EQUATION BY USING (G /G)-EXPANSION METHOD. A. Neamaty, B. Agheli, R. Acta Universitatis Apulensis ISSN: 1582-5329 http://wwwuabro/auajournal/ No 44/2015 pp 21-37 doi: 1017114/jaua20154403 EXACT SOLUTION TO TIME FRACTIONAL FIFTH-ORDER KORTEWEG-DE VRIES EQUATION BY USING

More information

Generalized bilinear differential equations

Generalized bilinear differential equations Generalized bilinear differential equations Wen-Xiu Ma Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA Abstract We introduce a kind of bilinear differential

More information

Maejo International Journal of Science and Technology

Maejo International Journal of Science and Technology Full Paper Maejo International Journal of Science and Technology ISSN 905-7873 Available online at www.mijst.mju.ac.th New eact travelling wave solutions of generalised sinh- ordon and ( + )-dimensional

More information

Solving the (3+1)-dimensional generalized KP and BKP equations by the multiple exp-function algorithm

Solving the (3+1)-dimensional generalized KP and BKP equations by the multiple exp-function algorithm Solving the (3+1)-dimensional generalized KP and BKP equations by the multiple exp-function algorithm Wen-Xiu Ma and Zuonong Zhu Department of Mathematics and Statistics, University of South Florida, Tampa,

More information

arxiv:nlin/ v1 [nlin.si] 25 Sep 2006

arxiv:nlin/ v1 [nlin.si] 25 Sep 2006 Remarks on the conserved densities of the Camassa-Holm equation Amitava Choudhuri 1, B. Talukdar 1a and S. Ghosh 1 Department of Physics, Visva-Bharati University, Santiniketan 73135, India Patha Bhavana,

More information

JACOBI ELLIPTIC FUNCTION EXPANSION METHOD FOR THE MODIFIED KORTEWEG-DE VRIES-ZAKHAROV-KUZNETSOV AND THE HIROTA EQUATIONS

JACOBI ELLIPTIC FUNCTION EXPANSION METHOD FOR THE MODIFIED KORTEWEG-DE VRIES-ZAKHAROV-KUZNETSOV AND THE HIROTA EQUATIONS JACOBI ELLIPTIC FUNCTION EXPANSION METHOD FOR THE MODIFIED KORTEWEG-DE VRIES-ZAKHAROV-KUZNETSOV AND THE HIROTA EQUATIONS ZAI-YUN ZHANG 1,2 1 School of Mathematics, Hunan Institute of Science Technology,

More information

Some New Traveling Wave Solutions of Modified Camassa Holm Equation by the Improved G'/G Expansion Method

Some New Traveling Wave Solutions of Modified Camassa Holm Equation by the Improved G'/G Expansion Method Mathematics and Computer Science 08; 3(: 3-45 http://wwwsciencepublishinggroupcom/j/mcs doi: 0648/jmcs080304 ISSN: 575-6036 (Print; ISSN: 575-608 (Online Some New Traveling Wave Solutions of Modified Camassa

More information

NEW PERIODIC WAVE SOLUTIONS OF (3+1)-DIMENSIONAL SOLITON EQUATION

NEW PERIODIC WAVE SOLUTIONS OF (3+1)-DIMENSIONAL SOLITON EQUATION Liu, J., et al.: New Periodic Wave Solutions of (+)-Dimensional Soliton Equation THERMAL SCIENCE: Year 7, Vol., Suppl., pp. S69-S76 S69 NEW PERIODIC WAVE SOLUTIONS OF (+)-DIMENSIONAL SOLITON EQUATION by

More information

Research Article The Extended Hyperbolic Function Method for Generalized Forms of Nonlinear Heat Conduction and Huxley Equations

Research Article The Extended Hyperbolic Function Method for Generalized Forms of Nonlinear Heat Conduction and Huxley Equations Journal of Applied Mathematics Volume 0 Article ID 769843 6 pages doi:0.55/0/769843 Research Article The Extended Hyperbolic Function Method for Generalized Forms of Nonlinear Heat Conduction and Huxley

More information

Available online at J. Math. Comput. Sci. 2 (2012), No. 1, ISSN:

Available online at   J. Math. Comput. Sci. 2 (2012), No. 1, ISSN: Available online at http://scik.org J. Math. Comput. Sci. 2 (2012), No. 1, 15-22 ISSN: 1927-5307 BRIGHT AND DARK SOLITON SOLUTIONS TO THE OSTROVSKY-BENJAMIN-BONA-MAHONY (OS-BBM) EQUATION MARWAN ALQURAN

More information

Application of fractional sub-equation method to the space-time fractional differential equations

Application of fractional sub-equation method to the space-time fractional differential equations Int. J. Adv. Appl. Math. and Mech. 4(3) (017) 1 6 (ISSN: 347-59) Journal homepage: www.ijaamm.com IJAAMM International Journal of Advances in Applied Mathematics and Mechanics Application of fractional

More information

The Exact Solitary Wave Solutions for a Family of BBM Equation

The Exact Solitary Wave Solutions for a Family of BBM Equation ISSN 749-3889(print),749-3897(online) International Journal of Nonlinear Science Vol. (2006) No., pp. 58-64 The Exact Solitary Wave Solutions f a Family of BBM Equation Lixia Wang, Jiangbo Zhou, Lihong

More information

Soliton solution of the Kadomtse-Petviashvili equation by homotopy perturbation method

Soliton solution of the Kadomtse-Petviashvili equation by homotopy perturbation method ISSN 1 746-7233, England, UK World Journal of Modelling and Simulation Vol. 5 (2009) No. 1, pp. 38-44 Soliton solution of the Kadomtse-Petviashvili equation by homotopy perturbation method H. Mirgolbabaei

More information

Elsayed M. E. Zayed 1 + (Received April 4, 2012, accepted December 2, 2012)

Elsayed M. E. Zayed 1 + (Received April 4, 2012, accepted December 2, 2012) ISSN 746-7659, England, UK Journal of Information and Computing Science Vol. 8, No., 03, pp. 003-0 A modified (G'/G)- expansion method and its application for finding hyperbolic, trigonometric and rational

More information

Restrictive Taylor Approximation for Gardner and KdV Equations

Restrictive Taylor Approximation for Gardner and KdV Equations Int. J. Adv. Appl. Math. and Mech. 1() (014) 1-10 ISSN: 47-59 Available online at www.ijaamm.com International Journal of Advances in Applied Mathematics and Mechanics Restrictive Taylor Approximation

More information

Lump solutions to dimensionally reduced p-gkp and p-gbkp equations

Lump solutions to dimensionally reduced p-gkp and p-gbkp equations Nonlinear Dyn DOI 10.1007/s11071-015-2539- ORIGINAL PAPER Lump solutions to dimensionally reduced p-gkp and p-gbkp equations Wen Xiu Ma Zhenyun Qin Xing Lü Received: 2 September 2015 / Accepted: 28 November

More information

The Modified Benjamin-Bona-Mahony Equation. via the Extended Generalized Riccati Equation. Mapping Method

The Modified Benjamin-Bona-Mahony Equation. via the Extended Generalized Riccati Equation. Mapping Method Applied Mathematical Sciences Vol. 6 0 no. 5495 55 The Modified Benjamin-Bona-Mahony Equation via the Extended Generalized Riccati Equation Mapping Method Hasibun Naher and Farah Aini Abdullah School of

More information

The superposition of algebraic solitons for the modified Korteweg-de Vries equation

The superposition of algebraic solitons for the modified Korteweg-de Vries equation Title The superposition of algebraic solitons for the modified Korteweg-de Vries equation Author(s) Chow, KW; Wu, CF Citation Communications in Nonlinear Science and Numerical Simulation, 14, v. 19 n.

More information

arxiv: v1 [math-ph] 17 Sep 2008

arxiv: v1 [math-ph] 17 Sep 2008 arxiv:080986v [math-ph] 7 Sep 008 New solutions for the modified generalized Degasperis Procesi equation Alvaro H Salas Department of Mathematics Universidad de Caldas Manizales Colombia Universidad Nacional

More information

Fibonacci tan-sec method for construction solitary wave solution to differential-difference equations

Fibonacci tan-sec method for construction solitary wave solution to differential-difference equations ISSN 1 746-7233, England, UK World Journal of Modelling and Simulation Vol. 7 (2011) No. 1, pp. 52-57 Fibonacci tan-sec method for construction solitary wave solution to differential-difference equations

More information

) -Expansion Method for Solving (2+1) Dimensional PKP Equation. The New Generalized ( G. 1 Introduction. ) -expansion method

) -Expansion Method for Solving (2+1) Dimensional PKP Equation. The New Generalized ( G. 1 Introduction. ) -expansion method ISSN 749-3889 (print, 749-3897 (online International Journal of Nonlinear Science Vol.4(0 No.,pp.48-5 The New eneralized ( -Expansion Method for Solving (+ Dimensional PKP Equation Rajeev Budhiraja, R.K.

More information

Computational Solutions for the Korteweg devries Equation in Warm Plasma

Computational Solutions for the Korteweg devries Equation in Warm Plasma COMPUTATIONAL METHODS IN SCIENCE AND TECHNOLOGY 16(1, 13-18 (1 Computational Solutions for the Korteweg devries Equation in Warm Plasma E.K. El-Shewy*, H.G. Abdelwahed, H.M. Abd-El-Hamid. Theoretical Physics

More information

A Numerical Solution of the Lax s 7 th -order KdV Equation by Pseudospectral Method and Darvishi s Preconditioning

A Numerical Solution of the Lax s 7 th -order KdV Equation by Pseudospectral Method and Darvishi s Preconditioning Int. J. Contemp. Math. Sciences, Vol. 2, 2007, no. 22, 1097-1106 A Numerical Solution of the Lax s 7 th -order KdV Equation by Pseudospectral Method and Darvishi s Preconditioning M. T. Darvishi a,, S.

More information

Analysis of Fractional Nonlinear Differential Equations Using the Homotopy Perturbation Method

Analysis of Fractional Nonlinear Differential Equations Using the Homotopy Perturbation Method Analysis of Fractional Nonlinear Differential Equations Using the Homotopy Perturbation Method Mehmet Ali Balcı and Ahmet Yıldırım Ege University, Department of Mathematics, 35100 Bornova-İzmir, Turkey

More information

Extended Jacobi Elliptic Function Expansion Method for Nonlinear Benjamin-Bona-Mahony Equations

Extended Jacobi Elliptic Function Expansion Method for Nonlinear Benjamin-Bona-Mahony Equations International Mathematical Forum, Vol. 7, 2, no. 53, 239-249 Extended Jacobi Elliptic Function Expansion Method for Nonlinear Benjamin-Bona-Mahony Equations A. S. Alofi Department of Mathematics, Faculty

More information

Periodic and Solitary Wave Solutions of the Davey-Stewartson Equation

Periodic and Solitary Wave Solutions of the Davey-Stewartson Equation Applied Mathematics & Information Sciences 4(2) (2010), 253 260 An International Journal c 2010 Dixie W Publishing Corporation, U. S. A. Periodic and Solitary Wave Solutions of the Davey-Stewartson Equation

More information

On The Exact Solution of Newell-Whitehead-Segel Equation Using the Homotopy Perturbation Method

On The Exact Solution of Newell-Whitehead-Segel Equation Using the Homotopy Perturbation Method On The Exact Solution of Newell-Whitehead-Segel Equation Using the Homotopy Perturbation Method S. Salman Nourazar, Mohsen Soori, Akbar Nazari-Golshan To cite this version: S. Salman Nourazar, Mohsen Soori,

More information

Complexiton Solutions of Nonlinear Partial Differential Equations Using a New Auxiliary Equation

Complexiton Solutions of Nonlinear Partial Differential Equations Using a New Auxiliary Equation British Journal of Mathematics & Computer Science 4(13): 1815-1826, 2014 SCIENCEDOMAIN international www.sciencedomain.org Complexiton Solutions of Nonlinear Partial Differential Equations Using a New

More information

Application of Laplace Adomian Decomposition Method for the soliton solutions of Boussinesq-Burger equations

Application of Laplace Adomian Decomposition Method for the soliton solutions of Boussinesq-Burger equations Int. J. Adv. Appl. Math. and Mech. 3( (05 50 58 (ISSN: 347-59 IJAAMM Journal homepage: www.ijaamm.com International Journal of Advances in Applied Mathematics and Mechanics Application of Laplace Adomian

More information

Exact Solutions for Generalized Klein-Gordon Equation

Exact Solutions for Generalized Klein-Gordon Equation Journal of Informatics and Mathematical Sciences Volume 4 (0), Number 3, pp. 35 358 RGN Publications http://www.rgnpublications.com Exact Solutions for Generalized Klein-Gordon Equation Libo Yang, Daoming

More information

exp Φ ξ -Expansion Method

exp Φ ξ -Expansion Method Journal of Applied Mathematics and Physics, 6,, 6-7 Published Online February 6 in SciRes. http://www.scirp.org/journal/jamp http://dx.doi.org/.6/jamp.6. Analytical and Traveling Wave Solutions to the

More information

Research Article Exact Solutions of φ 4 Equation Using Lie Symmetry Approach along with the Simplest Equation and Exp-Function Methods

Research Article Exact Solutions of φ 4 Equation Using Lie Symmetry Approach along with the Simplest Equation and Exp-Function Methods Abstract and Applied Analysis Volume 2012, Article ID 350287, 7 pages doi:10.1155/2012/350287 Research Article Exact Solutions of φ 4 Equation Using Lie Symmetry Approach along with the Simplest Equation

More information

The Homotopy Perturbation Method for Solving the Modified Korteweg-de Vries Equation

The Homotopy Perturbation Method for Solving the Modified Korteweg-de Vries Equation The Homotopy Perturbation Method for Solving the Modified Korteweg-de Vries Equation Ahmet Yildirim Department of Mathematics, Science Faculty, Ege University, 351 Bornova-İzmir, Turkey Reprint requests

More information

Derivation of Generalized Camassa-Holm Equations from Boussinesq-type Equations

Derivation of Generalized Camassa-Holm Equations from Boussinesq-type Equations Derivation of Generalized Camassa-Holm Equations from Boussinesq-type Equations H. A. Erbay Department of Natural and Mathematical Sciences, Faculty of Engineering, Ozyegin University, Cekmekoy 34794,

More information

An efficient algorithm on timefractional. equations with variable coefficients. Research Article OPEN ACCESS. Jamshad Ahmad*, Syed Tauseef Mohyud-Din

An efficient algorithm on timefractional. equations with variable coefficients. Research Article OPEN ACCESS. Jamshad Ahmad*, Syed Tauseef Mohyud-Din OPEN ACCESS Research Article An efficient algorithm on timefractional partial differential equations with variable coefficients Jamshad Ahmad*, Syed Tauseef Mohyud-Din Department of Mathematics, Faculty

More information

Variation of Parameters Method for Solving Fifth-Order. Boundary Value Problems

Variation of Parameters Method for Solving Fifth-Order. Boundary Value Problems Applied Mathematics & Information Sciences 2(2) (28), 135 141 An International Journal c 28 Dixie W Publishing Corporation, U. S. A. Variation of Parameters Method for Solving Fifth-Order Boundary Value

More information

KINK DEGENERACY AND ROGUE WAVE FOR POTENTIAL KADOMTSEV-PETVIASHVILI EQUATION

KINK DEGENERACY AND ROGUE WAVE FOR POTENTIAL KADOMTSEV-PETVIASHVILI EQUATION THERMAL SCIENCE, Year 05, Vol. 9, No. 4, pp. 49-435 49 KINK DEGENERACY AND ROGUE WAVE FOR POTENTIAL KADOMTSEV-PETVIASHVILI EQUATION by Hong-Ying LUO a*, Wei TAN b, Zheng-De DAI b, and Jun LIU a a College

More information

NEW EXACT SOLUTIONS OF SOME NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS VIA THE IMPROVED EXP-FUNCTION METHOD

NEW EXACT SOLUTIONS OF SOME NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS VIA THE IMPROVED EXP-FUNCTION METHOD www.arpapress.com/volumes/vol8issue2/ijrras_8_2_04.pdf NEW EXACT SOLUTIONS OF SOME NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS VIA THE IMPROVED EXP-FUNCTION METHOD M. F. El-Sabbagh, R. Zait and R. M. Abdelazeem

More information

-Expansion Method For Generalized Fifth Order KdV Equation with Time-Dependent Coefficients

-Expansion Method For Generalized Fifth Order KdV Equation with Time-Dependent Coefficients Math. Sci. Lett. 3 No. 3 55-6 04 55 Mathematical Sciences Letters An International Journal http://dx.doi.org/0.785/msl/03039 eneralized -Expansion Method For eneralized Fifth Order KdV Equation with Time-Dependent

More information

The (2+1) and (3+1)-Dimensional CBS Equations: Multiple Soliton Solutions and Multiple Singular Soliton Solutions

The (2+1) and (3+1)-Dimensional CBS Equations: Multiple Soliton Solutions and Multiple Singular Soliton Solutions The (+1) and (3+1)-Dimensional CBS Equations: Multiple Soliton Solutions and Multiple Singular Soliton Solutions Abdul-Majid Wazwaz Department of Mathematics, Saint Xavier University, Chicago, IL 60655,

More information

Breaking soliton equations and negative-order breaking soliton equations of typical and higher orders

Breaking soliton equations and negative-order breaking soliton equations of typical and higher orders Pramana J. Phys. (2016) 87: 68 DOI 10.1007/s12043-016-1273-z c Indian Academy of Sciences Breaking soliton equations and negative-order breaking soliton equations of typical and higher orders ABDUL-MAJID

More information

New Analytical Solutions For (3+1) Dimensional Kaup-Kupershmidt Equation

New Analytical Solutions For (3+1) Dimensional Kaup-Kupershmidt Equation International Conference on Computer Technology and Science (ICCTS ) IPCSIT vol. 47 () () IACSIT Press, Singapore DOI:.776/IPCSIT..V47.59 New Analytical Solutions For () Dimensional Kaup-Kupershmidt Equation

More information

Exact Solutions of Kuramoto-Sivashinsky Equation

Exact Solutions of Kuramoto-Sivashinsky Equation I.J. Education and Management Engineering 01, 6, 61-66 Published Online July 01 in MECS (http://www.mecs-press.ne DOI: 10.5815/ijeme.01.06.11 Available online at http://www.mecs-press.net/ijeme Exact Solutions

More information

EXACT TRAVELLING WAVE SOLUTIONS FOR NONLINEAR SCHRÖDINGER EQUATION WITH VARIABLE COEFFICIENTS

EXACT TRAVELLING WAVE SOLUTIONS FOR NONLINEAR SCHRÖDINGER EQUATION WITH VARIABLE COEFFICIENTS Journal of Applied Analysis and Computation Volume 7, Number 4, November 2017, 1586 1597 Website:http://jaac-online.com/ DOI:10.11948/2017096 EXACT TRAVELLIN WAVE SOLUTIONS FOR NONLINEAR SCHRÖDINER EQUATION

More information

Some Soliton Solutions of Non Linear Partial Differential Equations by Tan-Cot Method

Some Soliton Solutions of Non Linear Partial Differential Equations by Tan-Cot Method IOSR Journal of Mathematics (IOSR-JM) e-issn: 78-578,p-ISSN: 319-765X, 6, Issue 6 (May. - Jun. 013), PP 3-8 Some Soliton Solutions of Non Linear Partial Differential Equations by Tan-Cot Method Raj Kumar

More information

Solution of Linear and Nonlinear Schrodinger Equations by Combine Elzaki Transform and Homotopy Perturbation Method

Solution of Linear and Nonlinear Schrodinger Equations by Combine Elzaki Transform and Homotopy Perturbation Method American Journal of Theoretical and Applied Statistics 2015; 4(6): 534-538 Published online October 29, 2015 (http://wwwsciencepublishinggroupcom/j/ajtas) doi: 1011648/jajtas2015040624 ISSN: 2326-8999

More information

NEW EXTENDED (G /G)-EXPANSION METHOD FOR TRAVELING WAVE SOLUTIONS OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS (NPDEs) IN MATHEMATICAL PHYSICS

NEW EXTENDED (G /G)-EXPANSION METHOD FOR TRAVELING WAVE SOLUTIONS OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS (NPDEs) IN MATHEMATICAL PHYSICS italian journal of pure and applied mathematics n. 33 204 (75 90) 75 NEW EXTENDED (G /G)-EXPANSION METHOD FOR TRAVELING WAVE SOLUTIONS OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS (NPDEs) IN MATHEMATICAL

More information

Symbolic Computation and New Soliton-Like Solutions of the 1+2D Calogero-Bogoyavlenskii-Schif Equation

Symbolic Computation and New Soliton-Like Solutions of the 1+2D Calogero-Bogoyavlenskii-Schif Equation MM Research Preprints, 85 93 MMRC, AMSS, Academia Sinica, Beijing No., December 003 85 Symbolic Computation and New Soliton-Like Solutions of the 1+D Calogero-Bogoyavlenskii-Schif Equation Zhenya Yan Key

More information