Exact traveling wave solutions of nonlinear variable coefficients evolution equations with forced terms using the generalized.
|
|
- Jodie Banks
- 5 years ago
- Views:
Transcription
1 Exact traveling wave solutions of nonlinear variable coefficients evolution equations with forced terms using the generalized expansion method ELSAYED ZAYED Zagazig University Department of Mathematics Zagazig Egypt MAHMOUD ABDELAZIZ Zagazig University Department of Mathematics Zagazig Egypt Abstract: The exact traveling wave solutions of the nonlinear variable coefficients BurgersFisher equation and the generalized ardner equation with forced terms can be found in this article using the generalized expansion method. As a result, hyperbolic, trigonometric and rational function solutions with parameters are obtained. When these parameters are taken special values, the solitary wave solutions are derived from the hyperbolic function solutions. It is shown that the proposed method is direct, effective and can be applied to many other nonlinear evolution equations in the mathematical physics. Key Words: Nonlinear evolution equations; eneralized expansion method; Variable coefficients Burgers Fisher equation with the forced term; Variable coefficients generalized ardner equation with the forced term, Exact solutions. 1 Introduction The investigation of the exact solutions of nonlinear evolution equations NLEEs plays an important role in the study of nonlinear physical phenomena. It becomes one of the most exciting and extremely active areas of research investigation. In the past several decades, many effective methods for obtaining exact solutions of NLEEs have been presented, such as the inverse scattering method [1, the Hirota s bilinear method [, the Bäcklund transformation [3, the Painlevé expansion [4, the sinecosine method [5, the homogeneous balance method [6, the homotopy perturbation method [7 9, the variational iteration method [10 13, the Adomian decomposition method [14, the tanh function method [15,16, the algebraic method [17,18, the Jacobi elliptic function expansion method [19,0, the Fexpansion method [1,, the auxiliary equation method [3,4, the Expfunction method [5,6, the expansion method [7 4 and so on. However, to our knowledge, most of aforementioned methods are related to the constantcoefficient models. Recently, the study of variablecoefficients NLEEs is attracted much attention because most of real nonlinear physical equations possess variable coefficients. Very recently, Wang et al. [31 first introduced the expansion method to look for traveling wave solutions of NLEEs. This method is based on the assumptions that the traveling wave solutions can be expressed by a polynomial in, where satisfies the following second order linear ordinary differential equation: + λ + µ = 0, 1 and λ, µ are arbitrary constants. The objective of this article is to apply the generalized expansion method to improve the work made in [31. Zhang et al [35 first proposed the generalized expansion method to construct exact solutions of the mkdv equation with variable coefficients. As applications of the proposed method, we will consider the following two models: I. The nonlinear BurgersFisher equation with variable coefficients and forced term [3 has the form: u t dtu xx + uu x + u u = Rt, ISSN: Issue 3, Volume 10, March 011
2 where dt,, and Rt are arbitrary differentiable functions of t. The function Rt is called the forced term of Eq.. It is obvious that Eq. is the BurgersFisher equation for Rt = 0, dt, and are constants. It is the variable coefficient Fisher equation when dt = Rt = 0, which is used to describe nonlinear phenomena such as thermonuclear fusion and hydronium physics etc. It is also the variable coefficient Burgers equation when = Rt = 0, which often emerged in Mathematics and Physics. II. The nonlinear generalized ardner equation with variable coefficients and forced term has the form: u t + uu x + u u x + htu xxx + dtu x + ftu = F t, 3 where,, ht, dt, ft and F t are arbitrary differentiable functions of t. The function F t is called the forced term of Eq. 3. This equation is the variable coefficients generalized ardner equation when F t = 0, see reference [43. It is widely used in various branches of physics, such as plasma physics, fluid physics and quantum field theory. It also describes a variety of wave phenomena in plasma and solid state. Finally, it includes considerably interesting equations, such as KdV equation, mkdv equation and ardner equation. Description of the generalized expansion method For a given NLEE with independent variables X = x, y, z, t and dependent variable u, we consider the PDE Qu, u t, u x, u y, u z, u xt, u yt, u zt, u tt, u xx,... = 0. 4 The solution of Eq. 4 can be expressed by a polynomial in as follows: m i ux = α 0 X + α i X, i=1 α m X 0, 5 where = satisfies Eq. 1 while = X and α i X are all analytic functions of X to be determined later and d d. To determine ux explicitly, we consider the following four steps: Step1. Determine the positive integer m by balancing the highest order nonlinear terms and the highest order partial derivatives of ux in Eq. 4. Step. Substitute 5 along with Eq. 1 into Eq. 4 and collect all terms with the same order of together, the lefthand side of Eq. 4 is converted into a polynomial in. Then set each coefficient of this polynomial to zero to derive a set of overdetermined differential equations for α 0 X, α i X and X. Step3. Solve the system of overdetermined differential equations obtained in Step for α i X, i = 0, 1,..., m and X by the use of Maple or Mathematica. Step4. Use the results obtained in above steps to derive a series of fundamental solutions of Eq. 4 depending on since the solutions of Eq. 1 have been well known for us, then we can obtain the exact solutions of Eq Applications In this section, we determine the exact traveling wave solutions of the nonlinear BurgersFisher equation and the nonlinear generalized ardner equation with variablecoefficients and the forced terms which are attracted much attention. 3.1 Example 1. The variablecoefficient BurgersFisher equation with the forced term In order to obtain the exact solutions of Eq., we assume that the solution of this equation can be written in the form ux, t = υx, t + Rtdt, 6 where υx, t is a differentiable function of x, t while Rt is an integrable function of t. Substituting 6 ISSN: Issue 3, Volume 10, March 011
3 into Eq., we have υ xxx = α 1 tpt [ λ 3 υ t dtυ xx + υυ x + βtυ x { + υ + [βt 1 υ + [ 7λ + 8µ + λλ + 8µ where + βt [βt 1 = 0, 7 βt = Rtdt. 8 By balancing υ xx with υυ x in Eq. 7, we get m = 1. In order to search for explicit solutions, we suppose that Eq. 7 has the following formal solution: υx, t = α 0 t + α 1 t, α 1 t 0, 9 where = satisfies Eq. 1 and = ptx + qt. The functions pt and qt are differentiable functions of t to be determined. From 1 and 9 we have: υ t = α 1 t [xpt + qt {λα 1 t [xpt + qt α 1 t + µλ + µ, 13 where = d dt. Substituting 9 1 into Eq. 7 and collecting all terms with the same order of together, the lefthand side of Eq. 7 is converted into a polynomial in x i j, i = 0, 1, j = 0, 1,, 3. Setting each coefficient of this polynomial to zero, we get the following set of overdetermined differential equations: x 0 3 : dtα 1 tpt α 1 t pt = 0, x 0 : α 1 tqt 3λdtα 1 tpt λα 1 t pt + α 1 t α 1 tpt[α 0 t + βt = 0, µα 1 t [xpt + qt + α 0 t, 10 [ υ x = α 1 tpt + λ + µ, 11 υ xx = α 1 tpt [ 3 + 3λ [ + λ + µ + µλ, 1 x 0 1 : λα 1 tqt + α 1 t α 1 t λ + µdtα 1 tpt λα 1 tpt[α 0 t + βt µα 1 t pt +α 1 t[α 0 t + βt = 0, x 0 0 : µα 1 tqt + α 0 t ISSN: Issue 3, Volume 10, March 011
4 µλdtα 1 tpt + α 0 tβt µα 1 tpt[α 0 t + βt [ where St = d dt dt and c 1, c constants such that c 1 0. case. are arbitrary [α 0 t + βt + α 0 t +[α 0 t + βt = 0, α 0 t = c λ 1 4 [c λ 4µ 1 dt, x 1 : α 1 tpt = 0, x 1 1 : λα 1 tpt = 0, x 1 0 : µα 1 tpt = Solving the system 14 by the Maple or Mathematica, we have case1. α 0 t = c 1λdt c 1 λ 4µdt 1 α 1 t = c 1dt, pt = c 1, βt = 1 St dt { [St dt + 4c 1 λ 4µdt 1 dt qt = c 1 dt c 1 [ St dt dt, { [St dt, dt dt + c, α 1 t = c, pt = c 1, = c 1dt c, βt = 1 4 [c λ 4µ 1 qt = c dt + c 1 c dt, dtdt + c 3, =, dt = dt, 16 where c 1, c, c 3 are arbitrary constants such that c 1, c 0. Let us now write down the exact solutions corresponding to case1. The exact solutions corresponding to case are similar which are omitted here. Substituting 15 into 9, we have υx, t = c 1dt 1 4 { λ + { [St dt + 4c 1 λ 4µdt 1 dt. 17 Substituting 17 into 6, we have the solution of Eq. in the form ux, t = c 1dt { λ + =, =, dt = dt, { [St dt ISSN: Issue 3, Volume 10, March 011
5 where + 4c 1 λ 4µdt 1 dt + βt, = c 1 {x 1 dt dt [ St dt dt 18 + c. 19 From the general solution of Eq. 1 we can find the ratio. Consequently, we have the following exact solutions of Eq. : I If λ 4µ > 0, we obtain the hyperbolic function solution in the form ux, t = c 1dt λ 4µ A cosh λ 4µ +B sinh λ 4µ A sinh λ 4µ +B cosh λ 4µ 1 { [St 4 dt + 4c 1 λ 4µdt 1 dt + βt. 0 II If λ 4µ < 0, we have the trigonometric function solution in the form ux, t = c 1dt 4µ λ A sin 4µ λ +B cos 4µ λ A cos 4µ λ +B sin 4µ λ 1 { [St 4 dt 4c 1 4µ λ dt 1 dt + βt. 1 III If λ 4µ = 0, we get the rational function solution in the form ux, t = c 1 Bdt A + B + βt 1 { [St 1 dt, 4 dt where A and B are arbitrary constants. Finally, we note that, if µ = 0, λ > 0, B = 0 and A 0 then we deduce from 0 that ux, t = c 1λdt coth { [St λ + βt dt [ c1 λdt 1 dt, 3 while if µ = 0, λ > 0, B 0 and B > A then we deduce from 0 that ux, t = c 1λdt 1 4 tanh 0 + λ + βt { [St [ c1 λdt + dt 1 dt, 4 where 0 = tanh 1 A B. Note that 3 and 4 represent the solitary wave solutions of the Burgers Fisher equation. 3. Example. The generalized variablecoefficient ardner equation with the forced term In order to obtain the exact solutions of Eq. 3, we assume that the solution of this equation can be written in the form ux, t = ωx, t + F tdt, 5 ISSN: Issue 3, Volume 10, March 011
6 where ωx, t is a differentiable function of x, t while F t is an integrable function of t. Substituting 5 into Eq. 3, we have ω t + [ + ktωω x + ω ω x α 0 tα 1 tpt kt α 1 tpt[α 0 t + kt 7λ + 8µhtα 1 tpt 3 = 0, + [dt + kt + kt ω x where + htω xxx + ft[ω + kt = 0, 6 kt = F tdt. 7 By balancing ω xxx with ω ω x in Eq. 6, we get m = 1. In order to search for explicit solutions, we deduce that Eq. 6 has the same formal solution 9. Substituting 9 13 into Eq. 6 and collecting all terms with the same order of together, the lefthand side of Eq. 6 is converted into a polynomial in x i j, i = 0, 1, j = 0,..., 4. Setting each coefficient of this polynomial to zero, we get the following set of overdetermined differential equations: x 0 4 : α 1 t 3 pt 6htα 1 tpt 3 = 0, x 0 1 : λα 1 tqt λdtα 1 tpt λα 1 tpt[α 0 t + kt µα 1 t pt[α 0 t + kt λα 1 tpt[α 0 t + kt λλ + 8µhtα 1 tpt 3 λα 0 tα 1 tptkt +ftα 1 t µα 1 t pt +α 1 t = 0, x 0 3 : α 1 t pt λα 1 t 3 pt α 1 t pt[α 0 t + kt 1λhtα 1 tpt 3 = 0, x 0 0 : µα 1 tqt µλdtα 1 tpt µα 1 tpt[α 0 t + kt µλ + µhtα 1 tpt 3 µα 1 tpt[α 0 t + kt x 0 : α 1 tqt dtα 1 tpt λα 1 t pt α 1 tpt[α 0 t + kt +ft[α 0 t + kt µα 0 tα 1 tptkt +α 0 t = 0, µα 1 t 3 pt λα 1 t pt[α 0 t + kt x 1 : α 1 tpt = 0, ISSN: Issue 3, Volume 10, March 011
7 x 1 1 : λα 1 tpt = 0, x 1 0 : µα 1 tpt = 0. 8 Solving the system 8 by the Maple or Mathematica, we have [ ftkt α 0 t = c c 3 dt, α 1 t = c 3, pt = c 1, ht = c 3 6c, 1 = [c 3 λ c kt ftkt + dt, { [ ftkt qt = c 1 dt dt [c 3 c λ + kt + c 3 6 [ ftkt dt dt λ + µ + 6c 6c λ dt + c 3 c λ ktdt + kt dt dtdt, dt = dt, ft = ft, kt = kt, =, where = e ftdt and c 1, c, c 3 are arbitrary constants such that c 1, c 3 0. Substituting 9 into 9, we have 9 { ωx, t = c 3 + c c 3 ftkt dt. 30 Substituting 30 into 5, we have the solution of Eq. 3 in the form { ux, t = c 3 where + kt, = c 1 {x + + c c c 3 ftkt dt 31 [ ftkt dt dt + kt [c 3 c λ [ ftkt dt dt λ + µ + 6c 6c λ dt + c 3 c λ ktdt + kt dt dtdt. 3 Consequently, we have the following three types of exact solutions of Eq. 3: I If λ 4µ > 0, we obtain the hyperbolic function solution in the form { [ λ λ ux, t = c 3 + 4µ A cosh λ 4µ +B sinh λ 4µ A sinh λ 4µ +B cosh λ 4µ ftkt + c c 3 dt + kt. II If λ 4µ < 0, we have the trigonometric function solution in the form 33 ISSN: Issue 3, Volume 10, March 011
8 { [ λ 4µ λ ux, t = c 3 + A sin 4µ λ +B cos 4µ λ A cos 4µ λ +B sin 4µ λ ftkt + c c 3 dt + kt. 34 III If λ 4µ = 0, we get the rational function solution in the form [ ux, t = c 3 ftkt B A + B λ dt + kt. + c c 3 35 where A and B are arbitrary constants. Finally, we note that, if µ = 0, λ > 0, B = 0 and A 0 then we deduce from 33 that { [ c3 λ λ ux, t = 1 coth + c c 3 ftkt dt + kt, 36 while if µ = 0, λ > 0, B 0 and B > A then we deduce from 33 that { [ c3 λ ux, t = 1 tanh 0 + λ ftkt + c c 3 dt + kt, 37 where 0 = tanh 1 A B. Note that 36 and 37 represent the solitary wave solutions of the generalized ardner equation 3. Remark. All solutions of this article have been checked with the Maple by putting them back into the original equations and 3. 4 Conclusions In this article, the generalized expansion method is applied to obtain more general exact solutions for NLEEs. By using this method we have successfully obtained exact solutions with parameters of the variable coefficients BurgersFisher equation with the forced term and the variable coefficients generalized ardner equation with the forced term. When these parameters are taken special values, the solitary wave solutions are derived from the hyperbolic solutions. References: [1 M.J. Ablowitz, P.A. Clarkson, Soliton, Nonlinear Evolution Equations and Inverse Scattering, Cambridge Univ. Press, New York, [ R. Hirota, Exact solution of the Korteweg de Vries equation for multiple collisions of solitons, Phys. Rev. Lett [3 M.R. Miurs, Backlund Transformation, Springer, Berlin, [4 J. Weiss, M. Tabor,. Carnevale, The Painlevé property for partial differential equations, J. Math. Phys [5 C.T. Yan, A simple transformation for nonlinear waves, Phys. Lett. A [6 M.L. Wang, Exact solution for a compound KdV Burgers equations, Phys. Lett. A [7 M. ElShahed, Application of He s homotopy perturbation method to Volterra s integrodifferential equation, Int. J. Nonlinear Sci. Numer. Simul [8 J.H. He, Homotopy perturbation method for bifurcation of nonlinear problems, Int. J. Nonlinear Sci. Numer. Simul [9 J.H. He, Application of homotopy perturbation method to nonlinear wave equations, Chaos Solitons and Fractals [10 J.H. He, Variational iteration method a kind of nonlinear analytical technique: some examples, Int. J. Nonlinear Mech [11 J.H. He, Variational iteration method for autonomous ordinary differential systems, Appl. Math. Comput ISSN: Issue 3, Volume 10, March 011
9 [1 J.H. He, Variational principles for some nonlinear partial differential equations with variable coefficients, Chaos Solitons and Fractals [13 J.H. He, Variational approach to + 1 dimensional dispersive long water equations, Phys. Lett. A [14 T.A. Abassy, M.A. ElTawil, H.K. Saleh, The solution of KdV and mkdv equations using adomian Pade approximation, Int. J. Nonlinear Sci. Numer.Simul [15 E.M.E. Zayed, H.A. Zedan, K.A. epreel, roup analysis and modified extended Tanhfunction to find the invariant solutions and soliton solutions for nonlinear Euler equations, Int. J. Nonlinear Sci. Numer.Simul [16 H.A. Abdusalam, On an improved complex Tanhfunction method, Int. J. Nonlinear Sci. Numer. Simul [17 J.Q. Hu, An algebraic method exactly solving two high dimensional nonlinear evolution equations, Chaos Solitons and Fractals [18 Y. Chen, Q. Wang, B. Li, A series of solitonlike and doublelike periodic solutions of a + 1dimensional asymmetric Nizhnik Novikov Vesselov equation, Commun. Theor. Phys [19 S.K. Liu, Z.T. Fu, S.D. Liu, Q. Zhao, Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations, Phys. Lett. A [0 Z.T. Fu, S.K. Liu, S.D. Liu, Q. Zhao, New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations, Phys. Lett. A [1 J.B. Liu, K.Q. Yang, The extended Fexpansion method and exact solutions of nonlinear PDEs, Chaos Solitons and Fractals [ S. Zhang, New exact solutions of the KdV Burgers Kuramoto equation, Phys. Lett. A [3 S. Zhang, T.C. Xia, A generalized new auxiliary equation method and its applications to nonlinear partial differential equations, Phys. Lett. A [4 S. Zhang, T.C. Xia, A generalized auxiliary equation method and its application to + 1dimensional asymmetric Nizhnik Novikov Vesselov equations, J. Phys. A: Math. Theore [5 J.H. He, X.H. Wu, Expfunction method for nonlinear wave equations, Chaos Solitons and Fractals [6 J.H. He, M.A. Abdou, New periodic solutions for nonlinear evolution equations using Expfunction method, Chaos Solitons and Fractals [7 E.M.E. Zayed, K.A. epreel, The expansion method for finding travelling wave solutions of nonlinear PDEs in mathematical physics, J. Math. Phys [8 E.M.E. Zayed, K.A. epreel, Some applications of the expansion method to nonlinear partial differential equations, Appl. Math. Comput [9 E.M.E. Zayed, K.A. epreel, Three types of travelling wave solutions of nonlinear evolution equations using the expansion method, Int. J. Nonlinear Sci [30 E.M.E. Zayed, S. AlJoudi, Applications of an Improved expansion Method to Nonlinear PDEs in Mathematical Physics, AIP Conf. Proc. Amer. Institute of Phys [31 M.L. Wang, X.Z. Li, J.L. Zhang, The expansion method and traveling wave solutions of nonlinear evolution equations in mathematical physics, Phys. Lett. A [3 H. Zhang, D. Lu, Exact Solutions of the Variable Coefficient BurgersFisher Equation with Forced Term, Int. J. Nonlinear Sci [33 H. Zedan, New classes of solutions for a system of partial differential equations by expansion method, Nonlinear Sci. Lett. A, 1 3, [34 J. Zhang, X. Wei, Y. Lu, A generalized expansion method and its applications, Phys. Lett. A ISSN: Issue 3, Volume 10, March 011
10 [35 S. Zhang, J.L. Tong, W. Wang, A generalized expansion method for the mkdv equation with variable coefficients, Phys. Lett. A [36 S. Zhang, W. Wang and J.L. Tong, A generalized expansion method and its application to the +1dimensional Broer Kaup equations, Appl. Math. Comput [37 M. Song, Y. e, Application of the expansion method to 3+1dimensional nonlinear evolution equations, Comput. Math. Appl [38 E.M.E. Zayed, M.A.M. Abdelaziz, Exact Solutions for Nonlinear PDEs with Variable Coefficients Using the eneralized Expansion Method and the ExpFunction Method, Int. Rev. Phys [39 E.M.E. Zayed, M.A.M. Abdelaziz, Travelling wave solutions for the Burgers Equation and the KdV Equation with variable coefficients Using the eneralized Expansion Method, Z. Naturforsch. 65a 010 in press. [40 E.M.E. Zayed, M.A.M. Abdelaziz, Exact Solutions for The eneralized ZakharovKuznetsov Equation with Variable Coefficients Using The eneralized expansion method, AIP Conf. Proc. Amer. Institute of Phys [41 E.M.E. Zayed, S. AlJoudi, An Improved expansion Method for Solving Nonlinear PDEs in Mathematical Physics, AIP Conf. Proc. Amer. Institute of Phys [4 E.M.E. Zayed, Equivalence of The expansion Method and The TanhCoth Function Method, AIP Conf. Proc. Amer. Institute of Phys [43 L.H. Zhang, L.H. Dong, L.M. Yan, Construction of nontravelling wave solutions for the generalized variablecoefficient ardner equation, Appl. Math. Comput ISSN: Issue 3, Volume 10, March 011
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 information2. 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 informationModified 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 informationA 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 informationThe 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 informationThe 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 informationElsayed 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 informationNew 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 informationNew 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 informationTraveling Wave Solutions For Two Non-linear Equations By ( G G. )-expansion method
Traveling Wave Solutions For Two Non-linear Equations By ( )-expansion method Qinghua Feng Shandong University of Technology School of Science Zhangzhou Road 1, Zibo, 55049 China fqhua@sina.com Bin Zheng
More informationThe (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 informationImproved (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 informationTraveling Wave Solutions For The Fifth-Order Kdv Equation And The BBM Equation By ( G G
Traveling Wave Solutions For The Fifth-Order Kdv Equation And The BBM Equation By ( )-expansion method Qinghua Feng Shandong University of Technology School of Science Zhangzhou Road 1, Zibo, 55049 China
More informationThe 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 informationTraveling Wave Solutions For Three Non-linear Equations By ( G G. )-expansion method
Traveling Wave Solutions For Three Non-linear Equations By ( )-expansion method Qinghua Feng Shandong University of Technology School of Science Zhangzhou Road 1, Zibo, 55049 China fqhua@sina.com Bin Zheng
More informationNew Jacobi Elliptic Function Solutions for Coupled KdV-mKdV Equation
New Jacobi Elliptic Function Solutions for Coupled KdV-mKdV Equation Yunjie Yang Yan He Aifang Feng Abstract A generalized G /G-expansion method is used to search for the exact traveling wave solutions
More informationGeneralized and Improved (G /G)-Expansion Method Combined with Jacobi Elliptic Equation
Commun. Theor. Phys. 61 2014 669 676 Vol. 61, No. 6, June 1, 2014 eneralized and Improved /-Expansion Method Combined with Jacobi Elliptic Equation M. Ali Akbar, 1,2, Norhashidah Hj. Mohd. Ali, 1 and E.M.E.
More information-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 informationNew 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 informationTravelling 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 informationEXACT TRAVELING WAVE SOLUTIONS FOR NONLINEAR FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS USING THE IMPROVED (G /G) EXPANSION METHOD
Jan 4. Vol. 4 No. 7-4 EAAS & ARF. All rights reserved ISSN5-869 EXACT TRAVELIN WAVE SOLUTIONS FOR NONLINEAR FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS USIN THE IMPROVED ( /) EXPANSION METHOD Elsayed M.
More informationExact 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 informationHOMOTOPY 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 informationDepartment of Applied Mathematics, Dalian University of Technology, Dalian , China
Commun Theor Phys (Being, China 45 (006 pp 199 06 c International Academic Publishers Vol 45, No, February 15, 006 Further Extended Jacobi Elliptic Function Rational Expansion Method and New Families of
More informationRational Form Solitary Wave Solutions and Doubly Periodic Wave Solutions to (1+1)-Dimensional Dispersive Long Wave Equation
Commun. Theor. Phys. (Beijing, China) 43 (005) pp. 975 98 c International Academic Publishers Vol. 43, No. 6, June 15, 005 Rational Form Solitary Wave Solutions and Doubly Periodic Wave Solutions to (1+1)-Dimensional
More informationEXACT 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 informationAnalytic Solutions for A New Kind. of Auto-Coupled KdV Equation. with Variable Coefficients
Theoretical Mathematics & Applications, vol.3, no., 03, 69-83 ISSN: 79-9687 (print), 79-9709 (online) Scienpress Ltd, 03 Analytic Solutions for A New Kind of Auto-Coupled KdV Equation with Variable Coefficients
More informationNew 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 informationNew explicit solitary wave solutions for (2 + 1)-dimensional Boussinesq equation and (3 + 1)-dimensional KP equation
Physics Letters A 07 (00) 107 11 www.elsevier.com/locate/pla New explicit solitary wave solutions for ( + 1)-dimensional Boussinesq equation and ( + 1)-dimensional KP equation Yong Chen, Zhenya Yan, Honging
More informationHongliang Zhang 1, Dianchen Lu 2
ISSN 1749-3889 (print), 1749-3897 (online) International Journal of Nonlinear Science Vol.9(010) No.,pp.5-56 Exact Solutions of the Variable Coefficient Burgers-Fisher Equation with Forced Term Hongliang
More informationExact 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 informationPRAMANA 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 informationEXACT 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 informationA 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 informationAn Improved F-Expansion Method and Its Application to Coupled Drinfel d Sokolov Wilson Equation
Commun. Theor. Phys. (Beijing, China) 50 (008) pp. 309 314 c Chinese Physical Society Vol. 50, No., August 15, 008 An Improved F-Expansion Method and Its Application to Coupled Drinfel d Sokolov Wilson
More informationPeriodic 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 informationNew 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 informationNumerical 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 informationA Further Improved Tanh Function Method Exactly Solving The (2+1)-Dimensional Dispersive Long Wave Equations
Applied Mathematics E-Notes, 8(2008), 58-66 c ISSN 1607-2510 Available free at mirror sites of http://www.math.nthu.edu.tw/ amen/ A Further Improved Tanh Function Method Exactly Solving The (2+1)-Dimensional
More information) -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 informationSoliton solutions of Hirota equation and Hirota-Maccari system
NTMSCI 4, No. 3, 231-238 (2016) 231 New Trends in Mathematical Sciences http://dx.doi.org/10.20852/ntmsci.2016115853 Soliton solutions of Hirota equation and Hirota-Maccari system M. M. El-Borai 1, H.
More informationExact Solutions for a Fifth-Order Two-Mode KdV Equation with Variable Coefficients
Contemporary Engineering Sciences, Vol. 11, 2018, no. 16, 779-784 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ces.2018.8262 Exact Solutions for a Fifth-Order Two-Mode KdV Equation with Variable
More informationEXACT 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 informationOn Using the Homotopy Perturbation Method for Finding the Travelling Wave Solutions of Generalized Nonlinear Hirota- Satsuma Coupled KdV Equations
ISSN 1749-889 (print), 1749-897 (online) International Journal of Nonlinear Science Vol.7(2009) No.2,pp.159-166 On Using the Homotopy Perturbation Method for Finding the Travelling Wave Solutions of Generalized
More informationPainlevé analysis and some solutions of variable coefficient Benny equation
PRAMANA c Indian Academy of Sciences Vol. 85, No. 6 journal of December 015 physics pp. 1111 11 Painlevé analysis and some solutions of variable coefficient Benny equation RAJEEV KUMAR 1,, R K GUPTA and
More informationApplication 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 informationApplication 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 informationExact 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 informationMulti-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 informationAn 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 informationPeriodic and Soliton Solutions for a Generalized Two-Mode KdV-Burger s Type Equation
Contemporary Engineering Sciences Vol. 11 2018 no. 16 785-791 HIKARI Ltd www.m-hikari.com https://doi.org/10.12988/ces.2018.8267 Periodic and Soliton Solutions for a Generalized Two-Mode KdV-Burger s Type
More informationNo. 11 A series of new double periodic solutions metry constraint. For more details about the results of this system, the reader can find the
Vol 13 No 11, November 2004 cfl 2003 Chin. Phys. Soc. 1009-1963/2004/13(11)/1796-05 Chinese Physics and IOP Publishing Ltd A series of new double periodic solutions to a (2+1)-dimensional asymmetric Nizhnik
More informationA Generalized Extended F -Expansion Method and Its Application in (2+1)-Dimensional Dispersive Long Wave Equation
Commun. Theor. Phys. (Beijing, China) 6 (006) pp. 580 586 c International Academic Publishers Vol. 6, No., October 15, 006 A Generalized Extended F -Expansion Method and Its Application in (+1)-Dimensional
More informationMultiple-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 informationNew Application of the (G /G)-Expansion Method to Excite Soliton Structures for Nonlinear Equation
New Application of the /)-Expansion Method to Excite Soliton Structures for Nonlinear Equation Bang-Qing Li ac and Yu-Lan Ma b a Department of Computer Science and Technology Beijing Technology and Business
More informationNew Exact Traveling Wave Solutions of Nonlinear Evolution Equations with Variable Coefficients
Studies in Nonlinear Sciences (: 33-39, ISSN -39 IDOSI Publications, New Exact Traveling Wave Solutions of Nonlinear Evolution Equations with Variable Coefficients M.A. Abdou, E.K. El-Shewy and H.G. Abdelwahed
More informationMaejo 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 informationExact 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 informationPeriodic, 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 informationAuto-Bäcklund transformation and exact solutions for compound KdV-type and compound KdV Burgers-type equations with nonlinear terms of any order
Physics Letters A 305 (00) 377 38 www.elsevier.com/locate/pla Auto-Bäcklund transformation and exact solutions for compound KdV-type and compound KdV Burgers-type equations with nonlinear terms of any
More informationResearch Article A New Extended Jacobi Elliptic Function Expansion Method and Its Application to the Generalized Shallow Water Wave Equation
Journal of Applied Mathematics Volume 212, Article ID 896748, 21 pages doi:1.1155/212/896748 Research Article A New Extended Jacobi Elliptic Function Expansion Method and Its Application to the Generalized
More informationAn 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 informationApplication Of A Generalized Bernoulli Sub-ODE Method For Finding Traveling Solutions Of Some Nonlinear Equations
Application Of A Generalized Bernoulli Sub-ODE Method For Finding Traveling Solutions Of Some Nonlinear Equations Shandong University of Technology School of Science Zhangzhou Road 2, Zibo, 255049 China
More informationNEW 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 informationSome 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 informationSolitaryWaveSolutionsfortheGeneralizedZakharovKuznetsovBenjaminBonaMahonyNonlinearEvolutionEquation
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 informationA 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 informationExact Solutions for the Nonlinear PDE Describing the Model of DNA Double Helices using the Improved (G /G)- Expansion Method
Math Sci Lett 3, No, 107-113 014 107 Mathematical Sciences Letters An International Journal http://dxdoiorg/101785/msl/03006 Exact Solutions for the Nonlinear PDE Describing the Model of DNA Double Helices
More informationNew Exact Solutions to NLS Equation and Coupled NLS Equations
Commun. Theor. Phys. (Beijing, China 4 (2004 pp. 89 94 c International Academic Publishers Vol. 4, No. 2, February 5, 2004 New Exact Solutions to NLS Euation Coupled NLS Euations FU Zun-Tao, LIU Shi-Da,
More informationSoliton and Periodic Solutions to the Generalized Hirota-Satsuma Coupled System Using Trigonometric and Hyperbolic Function Methods.
ISSN 1749-889 (print), 1749-897 (online) International Journal of Nonlinear Science Vol.14(01) No.,pp.150-159 Soliton and Periodic Solutions to the Generalized Hirota-Satsuma Coupled System Using Trigonometric
More informationComputational 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 informationComplexiton 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 informationA 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 informationApplication 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 informationThe Riccati equation with variable coefficients expansion algorithm to find more exact solutions of nonlinear differential equations
MM Research Preprints, 275 284 MMRC, AMSS, Academia Sinica, Beijing No. 22, December 2003 275 The Riccati equation with variable coefficients expansion algorithm to find more exact solutions of nonlinear
More informationSymbolic 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 informationThe 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 informationExact Solutions For Fractional Partial Differential Equations By A New Generalized Fractional Sub-equation Method
Exact Solutions For Fractional Partial Differential Equations y A New eneralized Fractional Sub-equation Method QINHUA FEN Shandong University of Technology School of Science Zhangzhou Road 12, Zibo, 255049
More informationBreaking 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 informationSome 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 informationDouble Elliptic Equation Expansion Approach and Novel Solutions of (2+1)-Dimensional Break Soliton Equation
Commun. Theor. Phys. (Beijing, China) 49 (008) pp. 8 86 c Chinese Physical Society Vol. 49, No., February 5, 008 Double Elliptic Equation Expansion Approach and Novel Solutions of (+)-Dimensional Break
More informationHomotopy perturbation method for the Wu-Zhang equation in fluid dynamics
Journal of Physics: Conference Series Homotopy perturbation method for the Wu-Zhang equation in fluid dynamics To cite this article: Z Y Ma 008 J. Phys.: Conf. Ser. 96 08 View the article online for updates
More informationNew Solutions for Some Important Partial Differential Equations
ISSN 1749-3889 (print), 1749-3897 (online) International Journal of Nonlinear Science Vol.4(2007) No.2,pp.109-117 New Solutions for Some Important Partial Differential Equations Ahmed Hassan Ahmed Ali
More informationThe 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 informationSOLITON 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 informationTopological and Non-Topological Soliton Solutions of the Coupled Klein-Gordon-Schrodinger and the Coupled Quadratic Nonlinear Equations
Quant. Phys. Lett. 3, No., -5 (0) Quantum Physics Letters An International Journal http://dx.doi.org/0.785/qpl/0300 Topological Non-Topological Soliton Solutions of the Coupled Klein-Gordon-Schrodinger
More informationResearch 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 informationFibonacci 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 informationSolutions of the coupled system of Burgers equations and coupled Klein-Gordon equation by RDT Method
International Journal of Advances in Applied Mathematics and Mechanics Volume 1, Issue 2 : (2013) pp. 133-145 IJAAMM Available online at www.ijaamm.com ISSN: 2347-2529 Solutions of the coupled system of
More informationKeywords: Exp-function method; solitary wave solutions; modified Camassa-Holm
International Journal of Modern Mathematical Sciences, 2012, 4(3): 146-155 International Journal of Modern Mathematical Sciences Journal homepage:www.modernscientificpress.com/journals/ijmms.aspx ISSN:
More informationResearch 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 informationNEW 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 informationYong Chen a,b,c,qiwang c,d, and Biao Li c,d
Jacobi Elliptic Function Rational Expansion Method with Symbolic Computation to Construct New Doubly-periodic Solutions of Nonlinear Evolution Equations Yong Chen abc QiWang cd and Biao Li cd a Department
More informationEXACT SOLUTIONS OF NON-LINEAR FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS BY FRACTIONAL SUB-EQUATION METHOD
THERMAL SCIENCE, Year 15, Vol. 19, No. 4, pp. 139-144 139 EXACT SOLUTIONS OF NON-LINEAR FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS BY FRACTIONAL SUB-EQUATION METHOD by Hong-Cai MA a,b*, Dan-Dan YAO a, and
More informationThree types of generalized Kadomtsev Petviashvili equations arising from baroclinic potential vorticity equation
Chin. Phys. B Vol. 19, No. (1 1 Three types of generalized Kadomtsev Petviashvili equations arising from baroclinic potential vorticity equation Zhang Huan-Ping( 张焕萍 a, Li Biao( 李彪 ad, Chen Yong ( 陈勇 ab,
More informationThe 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 informationA multiple Riccati equations rational expansion method and novel solutions of the Broer Kaup Kupershmidt system
Chaos, Solitons and Fractals 30 (006) 197 03 www.elsevier.com/locate/chaos A multiple Riccati equations rational expansion method and novel solutions of the Broer Kaup Kupershmidt system Qi Wang a,c, *,
More informationSOLITARY 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 informationNew Formal Solutions of Davey Stewartson Equation via Combined tanh Function Method with Symmetry Method
Commun. Theor. Phys. Beijing China 7 007 pp. 587 593 c International Academic Publishers Vol. 7 No. April 5 007 New Formal Solutions of Davey Stewartson Equation via Combined tanh Function Method with
More informationPainlevé Test for the Certain (2+1)-Dimensional Nonlinear Evolution Equations. Abstract
Painlevé Test for the Certain (2+1)-Dimensional Nonlinear Evolution Equations T. Alagesan and Y. Chung Department of Information and Communications, Kwangju Institute of Science and Technology, 1 Oryong-dong,
More information