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Symbolic computation and exact traveling solutions for nonlinear partial differential equations 被引量：1

符号计算与非线性偏微分方程精确行波解(英文)
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摘要 In this paper, with the aid of the symbolic computation, a further extended tanh function method was presented. Based on the new general ansatz, many nonlinear partial differential equation（s）（NPDE（s）） can he solved. Especially, as applications, a compound KdV-mKdV equation and the Broer-Kaup equations are considered successfully, and many solutions including periodic solutions, triangle solutions, and rational solutions are obtained. The method can also be applied to other NPDEs. In this paper, with the aid of the symbolic computation, a further extended tanh function method was presented. Based on the new general ansatz, many nonlinear partial differential equation（s）（NPDE（s）） can he solved. Especially, as applications, a compound KdV-mKdV equation and the Broer-Kaup equations are considered successfully, and many solutions including periodic solutions, triangle solutions, and rational solutions are obtained. The method can also be applied to other NPDEs.
作者 吴国成 夏铁成
机构地区 Department of Mathematics Key Laboratory of Mathematics Mechanization
出处 《Journal of Shanghai University(English Edition)》 CAS 2008年第6期481-485,共5页 上海大学学报（英文版）
基金 supported by the Science Foundation of Shanghai Municipal Commission of Education (Grant No.06AZ081) the Science Foundation of Key Laboratory of Mathematics Mechanization (Grant No.KLMM0806) the shanghai Leading Academic Discipline Project (Grant No.J50101)
关键词 nonlinear partial differential equations （NPDEs） rational solution soliton solution doubly periodic solution Wu method nonlinear partial differential equations （NPDEs）, rational solution, soliton solution, doubly periodic solution, Wu method
分类号 O175.29 [理学—基础数学]
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参考文献10

  • 1Fan E G.Integrable System and Computer Algebra ([]..2004
  • 2Wang Q,Chen Y,Zhang H Q.A new Jacobi elliptic function rational expansion method and its application to (1+ 1)-dimensional dispersive long wave equation[].Chaos Solitons Fractals.2005
  • 3XIE F,YAN Z Y,ZHANG H Q.Explicit and exact travelingwave solutions of Whitham-Broer-Kaup shallow water equations[].Physics Letters.2001
  • 4He,J.H.Variational principles for some nonlinear partial differential equations with variable coefficients[].Chaos Solitons Fractals.2004
  • 5Li Xiaoyan,Yang Sen,Wang Mingliang.The periodic wave solutions for (3+1)-dimensional Klein-Gordon-Schrodinger equations[].Chaos Solitons Fractals.2005
  • 6He J H.Application of homotopy perturbation method to nonlinear wave equations〔J〕[].Chaos Solitons Fractals.2005
  • 7WANG Zhen,ZHANG Hong-qing.Soliton-like andperiodic form solutions to(2+1)-dimensional Todaequation[].Chaos Solitons Fractals.2007
  • 8Xia T C,Lii Z S,Zhang H Q.Symbolic computation and new families of exact soliton-like solutions of Konopelchenko-Dubrovsky equations[].Chaos Solitons Fractals.2004
  • 9S. Zhang.Symbolic computation and new families of exact non-travelling wave solutions of(2+1)-dimensional Konopelchenko-Dubrovsky equations[].Chaos Solitons Fractals.2007
  • 10Yan Zhen-ya.The Weierstrass elliptic function expansion method andits applications in nonlinear wave e-quations[].ChaosSolitons and Fractals.2006

同被引文献10

  • 1WANG M L.Solitary wave solutions for variant Boussinesq equations[J].Physics Letters A,1995,199(3-4):169-172.
  • 2HE J H.Variational principles for some nonlinear partial differential equations with variable coefficients[J].Chaos Solitons and Fractals,2004,19(4):84-851.
  • 3HU J Q.An algebraic method exactly solving two highdimensional nonlinear evolution equations[J].Chaos Solitons and Fractals,2005,23(2):391-398.
  • 4YAN C T.A simple transformation for nonlinear waves[J].Physics Letters A,1996,224(1-2):77-84.
  • 5LIU S K,FU Z T,LIU S D,ZHAO Q.Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations[J].Physics Letters A,2001,289(1-2):69-74.
  • 6FAN E G.Travelling wave solutions in terms of special functions for nonlinear coupled evolution systems[J].Physics Letters A,2002,300(2-3):243-249.
  • 7WANG M L,LI X Z,ZHANG J L.The (G'/G)-expansion method and travelling wave solutions of nonlinear evolution euqations in mathematical physics[J].Physics Letters A,2008,372(4):417-423.
  • 8ZHANG S,TONG J L,WANG W.A generalized (G'/G)expansion method for the mKdV equation with variable coefficients[J].Physics Letters A,2008,372(13):2254-2257.
  • 9WANG Z.Discrete tanh method for nonlinear differencedifferential equations[J].Computer Physics Communications,2009,180(7):1104-1108.
  • 10YAN Z Y.Envelope solution profiles of the discrete nonlinear Schr(o)dinger equation with a saturable nonlinearity[J].Applied Mathematics Letters,2009,22(4):448-452.

引证文献1

Journal of Shanghai University(English Edition)
2008年 第6期

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