中国物理B ›› 2006, Vol. 15 ›› Issue (10): 2210-2215.doi: 10.1088/1009-1963/15/10/004

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New exact solutions to some difference differential equations

王　振, 张鸿庆   

  1. Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China
  • 收稿日期:2005-07-12 修回日期:2006-06-02 出版日期:2006-10-20 发布日期:2006-10-20
  • 基金资助:
    Project supported by the State Key Development Program for Basic Research of China (Grant No 2004CB318000).

New exact solutions to some difference differential equations

Wang Zhen (王振)† and Zhang Hong-Qing(张鸿庆)   

  1. Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China
  • Received:2005-07-12 Revised:2006-06-02 Online:2006-10-20 Published:2006-10-20
  • Supported by:
    Project supported by the State Key Development Program for Basic Research of China (Grant No 2004CB318000).

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摘要： In this paper, we use our method to solve the extended Lotka--Volterra equation and discrete KdV equation. With the help of Maple, we obtain a number of exact solutions to the two equations including soliton solutions presented by hyperbolic functions of \sinh and \cosh, periodic solutions presented by trigonometric functions of \sin and \cos, and rational solutions. This method can be used to solve some other nonlinear difference--differential equations.

关键词: difference differential equation, soliton solutions, Lotka--Volterra equation, discrete KdV\\hbox{\hskip 1.9cm} equation

Abstract: In this paper, we use our method to solve the extended Lotka--Volterra equation and discrete KdV equation. With the help of Maple, we obtain a number of exact solutions to the two equations including soliton solutions presented by hyperbolic functions of sinh and cosh, periodic solutions presented by trigonometric functions of sin and cos, and rational solutions. This method can be used to solve some other nonlinear difference--differential equations.

Key words: difference differential equation, soliton solutions, Lotka--Volterra equation, discrete KdV equation

中图分类号:  (Ordinary differential equations)

  • 02.30.Hq
05.45.Yv (Solitons)