Recursion Operators of Two Supersymmetric Equations
|
|
- Patrick Hamilton
- 5 years ago
- Views:
Transcription
1 Commun. Theor. Phys ) Vol. 55, No. 2, February 15, 2011 Recursion Operators of Two Supersymmetric Equations LI Hong-Min Ó ), LI Biao ÓÂ), and LI Yu-Qi Ó ) Department of Mathematics, Ningbo University, Ningbo , China Received May 7, 2010; revised manuscript received June 24, 2010) Abstract From La representations, recursion operators for the supersymmetric KdV and the supersymmetric Kaup Kupershimdt SKK) equations are proposed eplicitly. Under some special conditions, the recursion operator of the supersymmetric Sawada Kotera equation can be recovered by the one of the SKK equation. PACS numbers: Ik, Pb Key words: supersymmetry, La representation, recursion operator 1 Introduction Supersymmetric integrable systems constitute a very interesting subject and as a consequence a number of well known integrable equations have been generalized into supersymmetric contet. 1 2] The supersymmetric etension of a nonlinear evolution equation KdV for instance) refers to a system of coupled equations for a bosonic field u, t) and a fermionic field φ, t) which reduces to the initial equation in the limit where the fermionic field is zero bosonic limit). In the classical contet, a fermionic field is described by an anticommuting function with values in an infinitely generated Grassmann algebra. However, supersymmetry is not just a coupling of a bosonic field to a fermionic field. It also implies that a transformation supersymmetry invariance) relating these two fields leaves the system invariant. So far, many methods in standard theory have been etended to this framework, such as Bäcklund transformations, 3] prolongation theory, 4 5] hamiltonian formalism, 6] grasmmannian description, 7] τ functions, 8] Darbou transformations, 9] bilinear approach, 10] etc. In order to have a mathematical formulation of these concepts we will consider the space of differential operators on a 1 1) superspace with coordinates, θ). These operators are polynomials in the supercovariant derivative D = θ + θ whose coefficients are superfields. The supercovariant derivative obeys D 2 =, where θ is the Grassmann variable and θ 2 = 0. Recently, Tian and Liu obtained an N = 1 supersymmetric Kaup-Kupershimdt SKK) equation and by a simple Miura-type transformation, they derived a supersymmetric Sawada Kotera SSK) equation and proposed the conserved quantities and recursion operator of it from supersymmetric La representation. 11] In Ref. 12], Popowicz also gave the supersymmetric SK equation from the Bi-Hamiltonian formulation and gave it s odd hamiltonian structure. But to our knowledge, the recursion operator of the SKK equation by Tian and Liu has not been investigated. With regard to the construction of the recursion operator for a given integrable system, there are several works devoted to this subject through some different ways. 138] On the basis of these ideas, Gürses et al. established an etremely simple, effective, and algorithmic method for the construction of recursion operators for nonlinear partial differential equations when the La representation is given. 19] In this paper, we will etend the method in Ref. 19] to obtain the recursion operator of the SSK equation. Then from the recursion operator of SKK equation, we successfully recover the recursion operator of SSK equation in Ref. 11]. At the same time, we also obtain the recursion operator of supersymmetric KdV SKdV) equation by this method. For convenience, the paper is organized as follows. In Sec. 2, we will calculate the recursion operators of the SKdV and SKK equations from their La representations. In Sec. 3, we present conclusions and some interesting open problems. 2 Recursion Operators of MRSKdV and SKK Equations 2.1 MRSKdV Equation From Ref. 20], we know if set L = D 4 +ΦD, from this it follows that L 3/2 + = D6 +3/2)ΦD 3 +3/4)Φ D, we get the SKdV: Φ t = 1 4 Φ ΦDΦ)), 1) Supported by Zhejiang Provincial Natural Science Foundations of China under Grant No. Y , National Natural Science Foundation of China under Grant Nos and , Ningbo Natural Science Foundation under Grant Nos. 2009B21003, 2010A and 2009B21003, and K.C. Wong Magna Fund in Ningbo University Corresponding author, biaolee2000@yahoo.com.cn c 2011 Chinese Physical Society and IOP Publishing Ltd
2 200 Communications in Theoretical Physics Vol. 55 which is the supersymmetric etension of the KdV equation found by Manin and Radul 21] by the same La representation. So Eq. 1) usually is also called MRSKdV equation. Furthermore, we find L = D L D, where D is a formal inverse to D, the adjoint operation is defind as D n ) = ) nn+1))/2 D n n Z), fg) = ) f g g f, for any f, g H, where H is the algebra of super pseudodifferentrial operators. According to Ref. 19], we can calculate the recursion operator through the following equality: L tn+4 = LL tn + R n, L], 2) where dφ/dt n = Φ tn = Φ n and so on, R n = LL) n/2) ) +. So we have R n = α + β)d + a + b. By equating the coefficients of powers of D in Eq. 2), we get α = 1 2 Φ n), β = 3 4 Φ n D Φ Φ n)), a = 1 2 Φ Φ n )), b = 0, 3) and the recursion operator for the MRSKdV equation: R = ΦD + 2DΦ) + Φ D + DΦ ) + DΦ)D Φ + 2Φ Φ ]. 4) Remark 1 It is necessary to point out that in Ref. 6], the recursion operator 4) had been obtained by the product of two hamiltonian operators. 20] 2.2 SKK Equation In Ref. 11], we know the SKK equation: u t + u + 5 uu u u3 + φ Du) φdu ) φφ 3 4 Dφ)2] = 0, φ t + φ + 5 uφ u φ u φ + u 2 φ φdφ ) 1 ] 2 Dφ)φ = 0 5) has the following La pair: L = 3 + u + φd + v, A = 9L 5/3 ) +, 6) where v = 1/2)u Dφ)). The L operator satisfies the reduction L = L, so we use the formula where L tn+6 = L 2 L tn + R n, L], 7) R n = α 5 + β 4 + γ 3 + δ 2 + ξ + η)d + a 5 + b 4 + c 3 + d 2 + e + f. 8) By equating the coefficients of the powers of D in Eq. 7), we obtain α = 0, β = 1 3 φ n ), γ = 5 3 φ n, δ = φ n + 4u φ n ) + uφ n ) + D φ φ n )) + 5φ u n ) + φu n )], ξ = 1 9 {26φ n + 14uφ n φd φ n ) + 4u + Dφ)] φ n) + 15φu n + 5φ u n), η = 1 27{ 28φn + 32uφ n + 2φDφ n ) + 212u Dφ)]φ n + 3D φ φ n ) + 2u 2 + 5u ) φ n) + 2u uφ n) 3φ Du) 2φ) φ n) + D 3uφ + 5φ ) φ n) + φ uφ n) + 2Du) + φ)d φ φ n))] + 30φu n + 25φ u n + 10φ u n) + D φ φu n)) 3φ φd u n )), a = 1 3 u n ), b = u n D φ n )], c = 1 18 {73u n + 10u u n) 2 φd u n )) 15Dφ n ) 2 Du) 2φ] φ n), d = 1 18 {81u n + 33uu n D φu n ) + 2φD u n ) + 53u Dφ)] u n ) 29Dφ n ) 4uD φ n ) D uφ n ) 7Du) φ n), e = 1 { 134un + 106uu n + 46φDu n ) + 92u 45Dφ)]u n + 3D φ u n ) 53Dφ ) 2u 2 7u ] u n ) 6u φd u n )) + u 2u 2 3Dφ ))u n 22φ + uφ)d u n ) + 2φD φd u n )) + 22φ Du)) φu n )] 78Dφ n ) 42uDφ n ) + φ 32Du)]φ n
3 No. 2 Communications in Theoretical Physics 201 9D Dφ)φ n ) 12u D φ n ) + 44φ 25Du )) φ n) + 7φ + Du ))φ n + 6Dφ )D φ n ) 2Du) 2φ) uφ n ) + 2φD Du) φ n )) 2Du)D φ φ n )] + 6u 2φ Du)) φ n )), f = 1 { 28un + 32uu n + 32φDu n ) + 68u 30Dφ)]u n + 38φ Du n ) + 63u + 4u 2 55Dφ )]u n + 8φ + uφ)du n ) + 37u + 18uu 35Dφ ) 12uDφ) + 13φDu)]u n + 2φ + 6uφ + φdφ) + 3u φ]d u n ) 2u D φu n ) 2φ D φd u n )) + 10φ Du) + 45u + 10u uu 10Dφ ) 10u Dφ) + 10φDu ) 10uDφ )] u n) + φ 3Du )] φu n) 3u Dφ )] φd u n )) 28Dφ n ) 32uDφ n ) 62Du) + 5φ]φ n + 49Dφ) 14u ]Dφ n ) 34Du ) + φ ]φ n 29u 39Dφ ) + 4u 2 ]Dφ n ) 78φ 9φu + 32Du ) + 12uDu)]φ n 5u 3Dφ ) Du)φ + 4uu ]D φ n ) 2u D uφ n ) 10Du ) 8uφ + 10u Du) 4φDφ) + 3u φ + 2φ + 7uDu )] φ n) + φ 3Du )] uφ n ) + 10φ 3Du )]D φ φ n )) 2φ D Du) φ n )) 3u Dφ )] Du) 2φ) φ n )). The recursion operator of SKK equation is found as R11 R 12 R = R 21 R 22 with R 11 = 1 + ), 9) { u 4 36u 3 49u + 18u 2 ) 2 35u + 60uu ) 118u 41uu 69 2 u2 8u 3) u u + 2u 2 ) 107u + 10uu + 25u u + 10u 2 u ) 6φD 3 21φ D 2 23φ + 6φu)D 6φDu) 11φ + 15uφ + 9φu + 6φDφ)]D + 198Dφ ) 12φDu ) 9φφ Dφ)2 + 21Du)φ ] 2φ + φ Dφ) φdφ ) + 5u φ + 6uφ + 3u φ + 2u 2 φ]d + 9Dφ )D φ + 3u D φ + 3φD Dφ ) + φd u + 2φD u 2 + 5φDu ) 5φφ 15φ Du ) 10φ Du) + 9Dφ)Dφ ) 10φuDu)] + Du ) + 2uDu) + 11φ 4uφ] φ 3u Dφ )) + 4φ + uφ)d φd + 2φD 2φ + uφ)d 2Du)D φ φ 4u φ + 2uφ)D + 2φD Du) φ φd φd ] + u 22φ Du) φ + 2φD φd ], R 12 = 1 { 60Du) Du ) uDu) + 19Du )] 60uu D + 7Du ) + 12uDu ) + 12u Du) + Du ) + 4uDu ) + 8u Du ) + 5u Du) + 2u 2 Du)] Du ) + 2uDu)] u + u Du ) 2u Du) u 215φ 3 18Dφ)D φ 2 45Dφ )D + 310φ 12φu) + 3 7Dφ ) + 12uDφ) 2φDu)]D + 280φ 57uφ + 27φu + 6Du)Dφ) 12φDφ)] + 4φDu ) + 9φφ + 3Dφ ) 7φ Du)
4 202 Communications in Theoretical Physics Vol. 55 R 21 = 1 + 6uDφ ) 6φDφ)]D + 16φ 32uφ + 31u φ + 4Dφ)Du ) 33φ Dφ) 2u φ 4u 2 φ + 4Du)Dφ ) 24φDφ )] 9u D Dφ) + 3Dφ )D u φd Du ) + 4Du) 9φ]D φ + 11φ + 4uφ) u + 7u φ + Du ) 18φ + 2uDu) 12uφ]D φ + 22φ uφ)d Du) + φd 12uφ 2Du)D 2Du) + φ]d φ φd Du)] 2Du)D φ u + 3uφ ) + 2Du) u 6Dφ )D ] + 6u Dφ )D + 2u + 2φD 2φD φ + 5Du)D φ 2φ Du)] u 24φDu), φ + 2u φd Du) Du)D φ] { 6φ 4 15φ 3 213φ + 3φu) 2 24φ 23uφ 27φu ) + 120φφ D + 12φ Dφ) + 29uφ + 92u φ 11φDφ ) 11φ + 45u φ] + 14φφ D + 15u φ 5Dφ )φ + 50u φ + 5φ Dφ) 2φ + 10uφ + 10u 2 φ + 45u φ ] φ 2uφ)D φ + 3φ D φ + 3u + Dφ ) 2uDφ)] φ + φ 2u 2 u 3Dφ )] + 2φ φd φ 2φ 2φ + uφ)d + 2Dφ)D φ φ + 2φ 2φ Du)] φ + 2Dφ) Dφ) φ, R 22 = 1 { u 4 24u 3 25u + 18u 2 ) 2 16u + 3uu ) 6u + 29uu u2 + 8u3) u + 6uu + 12u u + 8u 2 u ) u + 4uu ) u 6φD 3 + 6Dφ) 3 + φ D 2 Dφ ) φ 5uφ)D 22Dφ ) 3uDφ)] + 4φ 5uφ 7φu + 4φ φ + 6φDφ)]D 4Dφ ) + 3uDφ ) φdu ) 14φφ 15 2 Dφ)2 ] 3u Dφ) 82φ Du) + 3φu + φdφ ) + φ + 4u φ + 4uφ 2Dφ)φ + 2u 2 φ]d + Dφ ) 4uDφ ) 4u 7Dφ))Dφ ) + 3u 2u 2 )Dφ) + Du)φ + φ Du ) 2φDu ) + 14φφ ] + 4Dφ)D φ 15φ D Dφ) 2uφ + φ )D u] + Dφ ) + 2uDφ) 4φDu)] u + φ Du ) + 13φ ) + u + Dφ ) 4uu 2uDφ) 4φDu)]D φ + 2Dφ)D 2Du) + φ]d φ + 2Dφ)D φ u + 6Dφ)D uφ 2φ Du)D φ + 2φ φd Du) 2φ Du) 2φ] u. 10) Remark 2 In Eq. 9), if setting {u = DΦ), φ = Φ, the recursion operator of SSK equation 11] can be reproduced easily. Note that the classical recursion operator for the KK equation 19] is just the φ-independent part of R 11 : R 0 = 1 { u 4 36u 3 49u + 18u 2 ) 2 35u + 60uu ) 3 Conclusion + 118u 41uu 69 2 u2 8u 3) u u + 2u 2 ) 107u + 10uu + 25u u + 10u 2 u ). 11) In this work, the recursion operators of supersymmetic KdV and supersymmetric Kaup-Kupershimdt SKK)
5 No. 2 Communications in Theoretical Physics 203 equations are proposed eplicitly by their La representations. From the operator of SKK equation, the operator of supersymmetric Sawada-Kotera equation can be easily obtained by a simple transformation. However, when the order of recursion operator is high, it is a very hard and tedious work to compute the operator of supersymmetric equation by its La representations. Therefore, on the basis of symbolic computation system, it is a very useful work to establish a simple, effective, and algorithmic method for computing the recursion operator of supersymmetric equations. References 1] I.S. Krasil shchik and P.H.M. Kersten, Symmetries and Recursion Operators for Classical and Supersymmetric Differential Equations, Kluwer Acad. Publ., Dordrecht/Boston/London 2000). 2] Q.P. Liu and M. Manas, Supersymmetry and Integrable Systems, Springer, Berlin 1998); Q.P. Liu, Phys. Lett. A ) 335; Q.P. Liu, Commun. Theor. Phys ) ] M. Chaichain and P. Kulish, Phys. Lett. B ) ] G.H. Roelofs and P.H.M. Kersten, J. Math. Phys ) ] X.B. Hu, J. Phys. A: Math. Gen ) ] W. Oevel and Z. Popowicz, Commun. Math. Phys ) ] K. Ueno and H. Yamada, Adv. Stud. in Pure Math ) ] L.A. Ibort, L. Martinez Alonso, and E. Medina, J. Math. Phys ) ] Q.P. Liu and M. Manas, Phys. Lett. B ) ] Y.X. Yu, Commun. Theor. Phys ) ] K. Tian and Q.P. Liu, Phys. Lett. A ) ] Z. Popowicz, Phys. Lett. A ) ] L.A. Dickey, Soliton Equations and Hamiltonian Systems, 2nd ed. World Scientific, Singapore 2003). 14] A.S. Fokas and R.L. Anderson, J. Math. Phys ) ] A.S. Fokas, Stud. Appl. Math ) ] A.P. Fordy and J. Gibbons, J. Math. Phys ) ] P.M. Santini and A.S. Fokas, Commun. Math. Phys ) ] A.S. Fokas and P.M. Santini, Commun. Math. Phys ) ] M. Gürses, A. Karasu, and V.V. Sokolov, J. Math. Phys ) ] J.M. Figueroa-OºFarrill, J. Mas, and E. Ramos, Rev. Math. Phys ) 479; Integrability and Bihamiltonian Structure of the Even Order SKdV Hierarchies, Leuven Preprint KUL-TF-91/17 April 1991). 21] Yu.I. Manin and A.O. Radul, Commun. Math. Phys ) 65.
A supersymmetric Sawada-Kotera equation
A supersymmetric Sawada-Kotera equation arxiv:0802.4011v2 [nlin.si] 7 Dec 2008 Kai Tian and Q. P. Liu Department of Mathematics, China University of Mining and Technology, Beijing 100083, P.R. China Abstract
More informationNonlocal conservation laws for supersymmetric KdV equations
LAVAL-PHY-21/93 Nonlocal conservation laws for supersymmetric KdV equations arxiv:hep-th/9301080v1 19 Jan 1993 P. Dargis 1 and P. Mathieu 2 Département de Physique, Université Laval, Québec, Canada G1K
More informationSupersymmetric Sawada-Kotera Equation: Bäcklund-Darboux Transformations and. Applications
Supersymmetric Sawada-Kotera Equation: Bäcklund-Darboux Transformations and arxiv:1802.04922v1 [nlin.si] 14 Feb 2018 Applications Hui Mao, Q. P. Liu and Lingling Xue Department of Mathematics, China University
More informationExact Solutions of Supersymmetric KdV-a System via Bosonization Approach
Commun. Theor. Phys. 58 1 617 6 Vol. 58, No. 5, November 15, 1 Exact Solutions of Supersymmetric KdV-a System via Bosonization Approach GAO Xiao-Nan Ô é, 1 YANG Xu-Dong Êü, and LOU Sen-Yue 1,, 1 Department
More informationarxiv: v1 [nlin.si] 10 Oct 2011
A non-standard Lax formulation of the Harry Dym hierarchy and its supersymmetric extension arxiv:1110.2023v1 [nlin.si] 10 Oct 2011 Kai Tian 1, Ziemowit Popowicz 2 and Q. P. Liu 1 1 Department of Mathematics,
More informationDoes the Supersymmetric Integrability Imply the Integrability of Bosonic Sector?
Does the Supersymmetric Integrability Imply the Integrability of Bosonic Sector? Z I E M O W I T P O P O W I C Z Instytut Fizyki Teoretycznej Uniwersytet Wrocławski POLAND 15.07.2009-21.07.2009 Shihezi
More informationNew Integrable Decomposition of Super AKNS Equation
Commun. Theor. Phys. (Beijing, China) 54 (2010) pp. 803 808 c Chinese Physical Society and IOP Publishing Ltd Vol. 54, No. 5, November 15, 2010 New Integrable Decomposition of Super AKNS Equation JI Jie
More informationCrum Transformation and Wronskian Type Solutions for Supersymmetric KdV Equation
arxiv:solv-int/9701005v1 10 Jan 1997 Crum Transformation and Wronskian Type Solutions for Supersymmetric KdV Equation Q. P. Liu and M. Mañas Departamento de Física Teórica, Universidad Complutense E28040-Madrid,
More informationA New Integrable Couplings of Classical-Boussinesq Hierarchy with Self-Consistent Sources
Commun. Theor. Phys. Beijing, China 54 21 pp. 1 6 c Chinese Physical Society and IOP Publishing Ltd Vol. 54, No. 1, July 15, 21 A New Integrable Couplings of Classical-Boussinesq Hierarchy with Self-Consistent
More informationOn construction of recursion operators from Lax representation
On construction of recursion operators from Lax representation Metin Gürses, Atalay Karasu, and Vladimir V. Sokolov Citation: J. Math. Phys. 40, 6473 (1999); doi: 10.1063/1.533102 View online: http://dx.doi.org/10.1063/1.533102
More informationOn bosonic limits of two recent supersymmetric extensions of the Harry Dym hierarchy
arxiv:nlin/3139v2 [nlin.si] 14 Jan 24 On bosonic limits of two recent supersymmetric extensions of the Harry Dym hierarchy S. Yu. Sakovich Mathematical Institute, Silesian University, 7461 Opava, Czech
More informationarxiv: v1 [math-ph] 10 Sep 2015
A N = 2 etension of the Hirota bilinear formalism and the supersymmetric KdV equation arxiv:509.0337v [math-ph] 0 Sep 205 Laurent Delisle,2 September, 205 Abstract We present a bilinear Hirota representation
More informationN=2 supersymmetric unconstrained matrix GNLS hierarchies are consistent
ITP-UH-26/06 JINR-E2-2006-170 N=2 supersymmetric unconstrained matrix GNLS hierarchies are consistent arxiv:0708.1125v1 [nlin.si] 8 Aug 2007 F. Delduc a,1, O. Lechtenfeld b,2, and A.S. Sorin c,3 (a) Laboratoire
More informationSupersymmetric and Deformed Harry Dym Hierarchies
Supersymmetric and Deformed Harry Dym Hierarchies J. C. Brunelli a, Ashok Das b and Ziemowit Popowicz c arxiv:hep-th/03118v1 4 Nov 003 a Departamento de Física, CFM Universidade Federal de Santa Catarina
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 informationREFi INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS IC/92/70 THE BI-HAMILTONIAN STRUCTURES OF THE MANIN-RADUL SUPER KP HIERARCHY. Sudhakar Panda.
REFi IC/92/70 INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS THE BI-HAMILTONIAN STRUCTURES OF THE MANIN-RADUL SUPER KP HIERARCHY Sudhakar Panda and INTERNATIONAL ATOMIC ENERGY AGENCY Shibaji Roy UNITED NATIONS
More informationINTEGRABILITY AND BIHAMILTONIAN STRUCTURE OF THE EVEN ORDER SKdV HIERARCHIES
Preprint KUL TF 91/17 US FT/5-91 April 1991 INTEGRABILITY AND BIHAMILTONIAN STRUCTURE OF THE EVEN ORDER SKdV HIERARCHIES José M. Figueroa-O Farrill 1, Javier Mas 2, and Eduardo Ramos 1 1 Instituut voor
More informationOn Recursion Operator of the q-kp Hierarchy
Commun. Theor. Phys. 66 (2016 263 268 Vol. 66 No. 3 September 1 2016 On Recursion Operator of the -KP Hierarchy Ke-Lei Tian ( 田可雷 1 Xiao-Ming Zhu ( 朱晓鸣 1 and Jing-Song He ( 贺劲松 2 1 School of Mathematics
More informationA General Formula of Flow Equations for Harry Dym Hierarchy
Commun. Theor. Phys. 55 (211 193 198 Vol. 55, No. 2, February 15, 211 A General Formula of Flow Equations for Harry Dym Hierarchy CHENG Ji-Peng ( Î, 1 HE Jing-Song ( Ø, 2, and WANG Li-Hong ( 2 1 Department
More informationBäcklund transformation and special solutions for Drinfeld Sokolov Satsuma Hirota system of coupled equations
arxiv:nlin/0102001v1 [nlin.si] 1 Feb 2001 Bäcklund transformation and special solutions for Drinfeld Sokolov Satsuma Hirota system of coupled equations Ayşe Karasu (Kalkanli) and S Yu Sakovich Department
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 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 informationProlongation structure for nonlinear integrable couplings of a KdV soliton hierarchy
Prolongation structure for nonlinear integrable couplings of a KdV soliton hierarchy Yu Fa-Jun School of Mathematics and Systematic Sciences, Shenyang Normal University, Shenyang 110034, China Received
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 informationarxiv:nlin/ v1 [nlin.si] 7 Sep 2005
NONSINGULAR POSITON AND COMPLEXITON SOLUTIONS FOR THE COUPLED KDV SYSTEM arxiv:nlin/5918v1 [nlin.si] 7 Sep 25 H. C. HU 1,2, BIN TONG 1 AND S. Y. LOU 1,3 1 Department of Physics, Shanghai Jiao Tong University,
More informationCanonical Forms for BiHamiltonian Systems
Canonical Forms for BiHamiltonian Systems Peter J. Olver Dedicated to the Memory of Jean-Louis Verdier BiHamiltonian systems were first defined in the fundamental paper of Magri, [5], which deduced the
More informationExact Interaction Solutions of an Extended (2+1)-Dimensional Shallow Water Wave Equation
Commun. Theor. Phys. 68 (017) 165 169 Vol. 68, No., August 1, 017 Exact Interaction Solutions of an Extended (+1)-Dimensional Shallow Water Wave Equation Yun-Hu Wang ( 王云虎 ), 1, Hui Wang ( 王惠 ), 1, Hong-Sheng
More informationUniversity of Twente. Faculty of Mathematical Sciences. Deformation and recursion for the N =2α =1 supersymmetric KdV hierarchy. Memorandum No.
Faculty of Mathematical Sciences t University of Twente The Netherlands P.O. Box 17 7500 AE Enschede The Netherlands Phone: +31-53-4893400 Fax: +31-53-4893114 Email: memo@math.utwente.nl www.math.utwente.nl/publications
More informationGroup invariant solutions for the N = 2 super Korteweg-de Vries equation
Group invariant solutions for the N = 2 super Korteweg-de Vries equation M. A. Ayari V. Hussin P. Winternitz CRM-2556 July 1998 Centre de Recherches Mathématiques, Université de Montréal, C. P. 6128, Succ.
More informationSecond Order Lax Pairs of Nonlinear Partial Differential Equations with Schwarzian Forms
Second Order Lax Pairs of Nonlinear Partial Differential Equations with Schwarzian Forms Sen-yue Lou a b c, Xiao-yan Tang a b, Qing-Ping Liu b d, and T. Fukuyama e f a Department of Physics, Shanghai Jiao
More informationThe supersymmetric Camassa-Holm equation and geodesic flow on the superconformal group
J. Math. Phys. #8-0748 Third revision, October 000 The supersymmetric Camassa-Holm equation and geodesic flow on the superconformal group Chandrashekar Devchand 1, and Jeremy Schiff 3 1 Max-Planck-Institut
More informationInvariant Sets and Exact Solutions to Higher-Dimensional Wave Equations
Commun. Theor. Phys. Beijing, China) 49 2008) pp. 9 24 c Chinese Physical Society Vol. 49, No. 5, May 5, 2008 Invariant Sets and Exact Solutions to Higher-Dimensional Wave Equations QU Gai-Zhu, ZHANG Shun-Li,,2,
More informationOn recursion operators for elliptic models
On recursion operators for elliptic models D K Demskoi and V V Sokolov 2 School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia E-mail: demskoi@maths.unsw.edu.au
More informationA Method for Obtaining Darboux Transformations
Journal of Nonlinear Mathematical Physics 998, V.5, N, 40 48. Letter A Method for Obtaining Darbou Transformations Baoqun LU,YongHE and Guangjiong NI Department of Physics, Fudan University, 00433, Shanghai,
More informationA new integrable system: The interacting soliton of the BO
Phys. Lett., A 204, p.336-342, 1995 A new integrable system: The interacting soliton of the BO Benno Fuchssteiner and Thorsten Schulze Automath Institute University of Paderborn Paderborn & Germany Abstract
More informationThe rotating Morse potential energy eigenvalues solved by using the analytical transfer matrix method
Chin. Phys. B Vol. 21, No. 1 212 133 The rotating Morse potential energy eigenvalues solved by using the analytical transfer matrix method He Ying 何英, Tao Qiu-Gong 陶求功, and Yang Yan-Fang 杨艳芳 Department
More informationarxiv: v1 [nlin.si] 7 Oct 2013
A four-component Camassa-Holm type hierarchy arxiv:1310.1781v1 [nlin.si] 7 Oct 2013 Abstract Nianhua Li 1, Q. P. Liu 1, Z. Popowicz 2 1 Department of Mathematics China University of Mining and Technology
More informationA MULTI-COMPONENT LAX INTEGRABLE HIERARCHY WITH HAMILTONIAN STRUCTURE
Pacific Journal of Applied Mathematics Volume 1, Number 2, pp. 69 75 ISSN PJAM c 2008 Nova Science Publishers, Inc. A MULTI-COMPONENT LAX INTEGRABLE HIERARCHY WITH HAMILTONIAN STRUCTURE Wen-Xiu Ma Department
More informationApproximate Similarity Reduction for Perturbed Kaup Kupershmidt Equation via Lie Symmetry Method and Direct Method
Commun. Theor. Phys. Beijing, China) 54 2010) pp. 797 802 c Chinese Physical Society and IOP Publishing Ltd Vol. 54, No. 5, November 15, 2010 Approximate Similarity Reduction for Perturbed Kaup Kupershmidt
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 informationSymmetry Reductions of (2+1) dimensional Equal Width. Wave Equation
Authors: Symmetry Reductions of (2+1) dimensional Equal Width 1. Dr. S. Padmasekaran Wave Equation Asst. Professor, Department of Mathematics Periyar University, Salem 2. M.G. RANI Periyar University,
More informationSymmetry and Exact Solutions of (2+1)-Dimensional Generalized Sasa Satsuma Equation via a Modified Direct Method
Commun. Theor. Phys. Beijing, China 51 2009 pp. 97 978 c Chinese Physical Society and IOP Publishing Ltd Vol. 51, No., June 15, 2009 Symmetry and Exact Solutions of 2+1-Dimensional Generalized Sasa Satsuma
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 informationarxiv: v1 [nlin.si] 19 Dec 2017
Bilinear approach to Kuperschmidt super-kdv type equations Corina N. Babalic, A. S. Carstea, arxiv:171.06854v1 [nlin.si] 19 Dec 017 * Dept. of Theoretical Physics, Institute of Physics and Nuclear Engineering,
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 informationReductions to Korteweg-de Vries Soliton Hierarchy
Commun. Theor. Phys. (Beijing, China 45 (2006 pp. 23 235 c International Academic Publishers Vol. 45, No. 2, February 5, 2006 Reductions to Korteweg-de Vries Soliton Hierarchy CHEN Jin-Bing,,2, TAN Rui-Mei,
More informationLax Representations and Zero Curvature Representations by Kronecker Product
Lax Representations and Zero Curvature Representations by Kronecker Product arxiv:solv-int/9610008v1 18 Oct 1996 Wen-Xiu Ma and Fu-Kui Guo Abstract It is showed that Kronecker product can be applied to
More informationThe quasiclassical limit of the symmetry constraint of the KP hierarchy and the dispersionless KP hierarchy with self-consistent sources
Journal of Nonlinear Mathematical Physics Volume 13, Number 2 (2006), 193 204 Article The quasiclassical limit of the symmetry constraint of the KP hierarchy and the dispersionless KP hierarchy with self-consistent
More informationA Note on Nonclassical Symmetries of a Class of Nonlinear Partial Differential Equations and Compatibility
Commun. Theor. Phys. (Beijing, China) 52 (2009) pp. 398 402 c Chinese Physical Society and IOP Publishing Ltd Vol. 52, No. 3, September 15, 2009 A Note on Nonclassical Symmetries of a Class of Nonlinear
More informationarxiv:hep-th/ v2 21 May 1993
N=2 SUPER BOUSSINESQ HIERARCHY: LAX PAIRS AND CONSERVATION LAWS LNF-93/022 (P) BONN-HE-93-18 hep-th/9305078 May 1993 arxiv:hep-th/9305078v2 21 May 1993 S.Bellucci a, E.Ivanov b,c, S.Krivonos a,c and A.Pichugin
More informationVirasoro constraints and W-constraints for the q-kp hierarchy
Virasoro constraints and W-constraints for the q-kp hierarchy Kelei Tian XŒX Jingsong He å t University of Science and Technology of China Ningbo University July 21, 2009 Abstract Based on the Adler-Shiota-van
More informationEXACT SOLITARY WAVE AND PERIODIC WAVE SOLUTIONS OF THE KAUP-KUPERSCHMIDT EQUATION
Journal of Applied Analysis and Computation Volume 5, Number 3, August 015, 485 495 Website:http://jaac-online.com/ doi:10.11948/015039 EXACT SOLITARY WAVE AND PERIODIC WAVE SOLUTIONS OF THE KAUP-KUPERSCHMIDT
More informationSolutions of the nonlocal nonlinear Schrödinger hierarchy via reduction
Solutions of the nonlocal nonlinear Schrödinger hierarchy via reduction Kui Chen, Da-jun Zhang Department of Mathematics, Shanghai University, Shanghai 200444, P.R. China June 25, 208 arxiv:704.0764v [nlin.si]
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 informationToward Analytic Solution of Nonlinear Differential Difference Equations via Extended Sensitivity Approach
Commun. Theor. Phys. 57 (2012) 5 9 Vol. 57, No. 1, January 15, 2012 Toward Analytic Solution of Nonlinear Differential Difference Equations via Extended Sensitivity Approach G. Darmani, 1, S. Setayeshi,
More informationThe Complete Set of Generalized Symmetries for the Calogero Degasperis Ibragimov Shabat Equation
Proceedings of Institute of Mathematics of NAS of Ukraine 2002, Vol. 43, Part 1, 209 214 The Complete Set of Generalized Symmetries for the Calogero Degasperis Ibragimov Shabat Equation Artur SERGYEYEV
More informationBoussineq-Type Equations and Switching Solitons
Proceedings of Institute of Mathematics of NAS of Ukraine, Vol. 3, Part 1, 3 351 Boussineq-Type Equations and Switching Solitons Allen PARKER and John Michael DYE Department of Engineering Mathematics,
More informationNonlinear Analysis. Variational identities and applications to Hamiltonian structures of soliton equations
Nonlinear Analysis 71 (2009) e1716 e1726 Contents lists available at ScienceDirect Nonlinear Analysis journal homepage: www.elsevier.com/locate/na Variational identities and applications to Hamiltonian
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 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 informationUniversidad del Valle. Equations of Lax type with several brackets. Received: April 30, 2015 Accepted: December 23, 2015
Universidad del Valle Equations of Lax type with several brackets Raúl Felipe Centro de Investigación en Matemáticas Raúl Velásquez Universidad de Antioquia Received: April 3, 215 Accepted: December 23,
More informationPoisson-Lie T-Duality and supermanifolds
Poisson-Lie T-Duality and supermanifolds L. Hlavatý, I. Petr, V. Štěpán, J. Vysoký Department of Physics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague IPM
More informationarxiv:nlin/ v2 [nlin.si] 14 Sep 2001
Second order Lax pairs of nonlinear partial differential equations with Schwarz variants arxiv:nlin/0108045v2 [nlin.si] 14 Sep 2001 Sen-yue Lou 1,2,3, Xiao-yan Tang 2,3, Qing-Ping Liu 1,4,3 and T. Fukuyama
More informationarxiv: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 informationBose Description of Pauli Spin Operators and Related Coherent States
Commun. Theor. Phys. (Beijing, China) 43 (5) pp. 7 c International Academic Publishers Vol. 43, No., January 5, 5 Bose Description of Pauli Spin Operators and Related Coherent States JIANG Nian-Quan,,
More informationMultisolitonic solutions from a Bäcklund transformation for a parametric coupled Korteweg-de Vries system
arxiv:407.7743v3 [math-ph] 3 Jan 205 Multisolitonic solutions from a Bäcklund transformation for a parametric coupled Korteweg-de Vries system L. Cortés Vega*, A. Restuccia**, A. Sotomayor* January 5,
More informationBoundary value problems for integrable equations compatible with the symmetry algebra
Boundary value problems for integrable equations compatible with the symmetry algebra Burak Gürel, Metin Gürses, and Ismagil Habibullin Citation: J. Math. Phys. 36, 6809 (1995); doi: 10.1063/1.531189 View
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 informationIntroduction to the Hirota bilinear method
Introduction to the Hirota bilinear method arxiv:solv-int/9708006v1 14 Aug 1997 J. Hietarinta Department of Physics, University of Turku FIN-20014 Turku, Finland e-mail: hietarin@utu.fi Abstract We give
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 informationUniversal Associated Legendre Polynomials and Some Useful Definite Integrals
Commun. Theor. Phys. 66 0) 158 Vol. 66, No., August 1, 0 Universal Associated Legendre Polynomials and Some Useful Definite Integrals Chang-Yuan Chen í ), 1, Yuan You ), 1 Fa-Lin Lu öß ), 1 Dong-Sheng
More informationGeneralized Burgers equations and Miura Map in nonabelian ring. nonabelian rings as integrable systems.
Generalized Burgers equations and Miura Map in nonabelian rings as integrable systems. Sergey Leble Gdansk University of Technology 05.07.2015 Table of contents 1 Introduction: general remarks 2 Remainders
More informationDynamics of solitons of the generalized (3+1)-dimensional nonlinear Schrödinger equation with distributed coefficients
Dynamics of solitons of the generalized (3+1-dimensional nonlinear Schrödinger equation with distributed coefficients Liu Xiao-Bei( and Li Biao( Nonlinear Science Center and Department of Mathematics,
More informationGrammian and Pfaffian solutions as well as Pfaffianization for a (3+1)-dimensional generalized shallow water equation
Grammian and Pfaffian solutions as well as Pfaffianization for a (3+1)-dimensional generalized shallow water equation Tang Ya-Ning( 唐亚宁 ) a), Ma Wen-Xiu( 马文秀 ) b), and Xu Wei( 徐伟 ) a) a) Department of
More informationarxiv: v1 [nlin.si] 23 Aug 2007
arxiv:0708.3247v1 [nlin.si] 23 Aug 2007 A new integrable generalization of the Korteweg de Vries equation Ayşe Karasu-Kalkanlı 1), Atalay Karasu 2), Anton Sakovich 3), Sergei Sakovich 4), Refik Turhan
More informationarxiv: v2 [math-ph] 18 Aug 2014
QUANTUM TORUS SYMMETRY OF THE KP, KDV AND BKP HIERARCHIES arxiv:1312.0758v2 [math-ph] 18 Aug 2014 CHUANZHONG LI, JINGSONG HE Department of Mathematics, Ningbo University, Ningbo, 315211 Zhejiang, P.R.China
More information7 Yang Hong-Xiang et al Vol. 4 The present paper is devoted to introducing the loop algebra ~, from which the real form of the KN hierarchy is derived
Vol 4 No 5, May 25 cfl 25 hin. Phys. Soc. 9-963/25/4(5)/69-6 hinese Physics and IOP Publishing Ltd class of integrable expanding model for the coupled KNS Kaup Newell soliton hierarchy * Yang Hong-Xiang(Ξ
More informationNonlocal Symmetry and Interaction Solutions of a Generalized Kadomtsev Petviashvili Equation
Commun. Theor. Phys. 66 (2016) 189 195 Vol. 66 No. 2 August 1 2016 Nonlocal Symmetry and Interaction Solutions of a Generalized Kadomtsev Petviashvili Equation Li-Li Huang (áûû) 1 Yong Chen (í ) 1 and
More informationSUB-MANIFOLD AND TRAVELING WAVE SOLUTIONS OF ITO S 5TH-ORDER MKDV EQUATION
Journal of Applied Analysis and Computation Volume 7, Number 4, November 07, 47 430 Website:http://jaac-online.com/ DOI:0.94/0706 SUB-MANIFOLD AND TRAVELING WAVE SOLUTIONS OF ITO S 5TH-ORDER MKDV EQUATION
More informationNew Homoclinic and Heteroclinic Solutions for Zakharov System
Commun. Theor. Phys. 58 (2012) 749 753 Vol. 58, No. 5, November 15, 2012 New Homoclinic and Heteroclinic Solutions for Zakharov System WANG Chuan-Jian ( ), 1 DAI Zheng-De (à ), 2, and MU Gui (½ ) 3 1 Department
More informationResearch Article. Yehui Huang, 1 Yuqin Yao, 2 and Yunbo Zeng Introduction
Advances in Mathematical Physics Volume 015 Article ID 3973 11 pages http://ddoiorg/101155/015/3973 Research Article Links between (γ n σ k )-KP Hierarchy (γ n σ k )-mkp Hierarchy and (1)-(γ n σ k )-Harry
More informationInfinite Sequence Soliton-Like Exact Solutions of (2 + 1)-Dimensional Breaking Soliton Equation
Commun. Theor. Phys. 55 (0) 949 954 Vol. 55, No. 6, June 5, 0 Infinite Sequence Soliton-Like Exact Solutions of ( + )-Dimensional Breaking Soliton Equation Taogetusang,, Sirendaoerji, and LI Shu-Min (Ó
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 informationIntegrable Rosochatius Deformations for an Integrable Couplings of CKdV Equation Hierarchy
Commun. Theor. Phys. Beiing, China 54 00 pp. 609 64 c Chinese Physical Society and IOP Publishing Ltd Vol. 54, No. 4, October 5, 00 Integrable Rosochatius Deformations for an Integrable Couplings of CKdV
More informationLattice geometry of the Hirota equation
Lattice geometry of the Hirota equation arxiv:solv-int/9907013v1 8 Jul 1999 Adam Doliwa Instytut Fizyki Teoretycznej, Uniwersytet Warszawski ul. Hoża 69, 00-681 Warszawa, Poland e-mail: doliwa@fuw.edu.pl
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 Local Time-Dependent Symmetries of Integrable Evolution Equations
Proceedings of Institute of Mathematics of NAS of Ukraine 2000, Vol. 30, Part 1, 196 203. On Local Time-Dependent Symmetries of Integrable Evolution Equations A. SERGYEYEV Institute of Mathematics of the
More informationRESEARCH ARTICLE. A symbolic algorithm for computing recursion operators of nonlinear PDEs
International Journal of Computer Mathematics Vol. 00, No. 00, Month 200, 1 27 RESEARCH ARTICLE A symbolic algorithm for computing recursion operators of nonlinear PDEs D.E. Baldwin and W. Hereman Department
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 informationComplete integrability of a modified vector derivative nonlinear Schrödinger equation
Complete integrability of a modified vector derivative nonlinear Schrödinger equation arxiv:solv-int/9407002v1 14 Jul 1994 Ralph Willox 1, Willy Hereman 2 and Frank Verheest 3 1 Dienst Theoretische Natuurkunde,
More informationIntegration of Bi-Hamiltonian Systems by Using the Dressing Method
Proceedings of Institute of Mathematics of NAS of Ukraine 2004, Vol. 50, Part 1, 319 324 Integration of Bi-Hamiltonian Systems by Using the Dressing Method Yuriy BERKELA Carpathian Biosphere Reserve, Rakhiv,
More informationTHE LAX PAIR FOR THE MKDV HIERARCHY. Peter A. Clarkson, Nalini Joshi & Marta Mazzocco
Séminaires & Congrès 14, 006, p. 53 64 THE LAX PAIR FOR THE MKDV HIERARCHY by Peter A. Clarkson, Nalini Joshi & Marta Mazzocco Abstract. In this paper we give an algorithmic method of deriving the Lax
More informationJournal of Geometry and Physics
Journal of Geometry and Physics 07 (206) 35 44 Contents lists available at ScienceDirect Journal of Geometry and Physics journal homepage: www.elsevier.com/locate/jgp Multi-component generalization of
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 informationSYMBOLIC SOFTWARE FOR SOLITON THEORY: INTEGRABILITY, SYMMETRIES CONSERVATION LAWS AND EXACT SOLUTIONS. Willy Hereman
. SYMBOLIC SOFTWARE FOR SOLITON THEORY: INTEGRABILITY, SYMMETRIES CONSERVATION LAWS AND EXACT SOLUTIONS Willy Hereman Dept. of Mathematical and Computer Sciences Colorado School of Mines Golden, Colorado
More informationarxiv:solv-int/ v1 31 Oct 1997
Darboux Transformations for SUSY Integrable Systems Q. P. Liu and Manuel Mañas arxiv:solv-int/9711002v1 31 Oct 1997 Departamento de Física Teórica, Universidad Complutense, E28040-Madrid, Spain. Abstract.
More informationSolving ground eigenvalue and eigenfunction of spheroidal wave equation at low frequency by supersymmetric quantum mechanics method
Chin. Phys. B Vol. 0, No. (0) 00304 Solving ground eigenvalue eigenfunction of spheroidal wave equation at low frequency by supersymmetric quantum mechanics method Tang Wen-Lin( ) Tian Gui-Hua( ) School
More informationRecursion operators of some equations of hydrodynamic type
Recursion operators of some equations of hydrodynamic type M. Gürses and K. Zheltukhin Citation: J. Math. Phys. 4, 309 (00); doi: 0.063/.346597 View online: http://dx.doi.org/0.063/.346597 View Table of
More informationA new four-dimensional chaotic system
Chin. Phys. B Vol. 19 No. 12 2010) 120510 A new four-imensional chaotic system Chen Yong ) a)b) an Yang Yun-Qing ) a) a) Shanghai Key Laboratory of Trustworthy Computing East China Normal University Shanghai
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 information