中国物理B ›› 2004, Vol. 13 ›› Issue (12): 2008-2012.doi: 10.1088/1009-1963/13/12/006

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A general mapping approach and new travelling wave solutions to the general variable coefficient KdV equation

朱加民1, 马正义1, 郑春龙2   

  1. (1)Department of Physics, Lishui College, Lishui 323000, China; (2)Department of Physics, Lishui College, Lishui 323000, China; Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
  • 收稿日期:2004-04-01 修回日期:2004-06-23 出版日期:2004-12-17 发布日期:2005-03-17
  • 基金资助:
    Project supported by the Natural Science Foundation of Zhejiang Province, China (Grant No 100039).

A general mapping approach and new travelling wave solutions to the general variable coefficient KdV equation

Zhu Jia-Min (朱加民)a, Zheng Chun-Long (郑春龙)ab, Ma Zheng-Yi (马正义)a   

  1. a Department of Physics, Lishui College, Lishui 323000, China; b Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
  • Received:2004-04-01 Revised:2004-06-23 Online:2004-12-17 Published:2005-03-17
  • Supported by:
    Project supported by the Natural Science Foundation of Zhejiang Province, China (Grant No 100039).

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摘要： A general mapping deformation method is applied to a generalized variable coefficient KdV equation. Many new types of exact solutions, including solitary wave solutions, periodic wave solutions, Jacobian and Weierstrass doubly periodic wave solutions and other exact excitations are obtained by the use of a simple algebraic transformation relation between the generalized variable coefficient KdV equation and a generalized cubic nonlinear Klein－Gordon equation.

关键词: generalized variable coefficient KdV equation, general mapping approach, travelling wave solution

Abstract: A general mapping deformation method is applied to a generalized variable coefficient KdV equation. Many new types of exact solutions, including solitary wave solutions, periodic wave solutions, Jacobian and Weierstrass doubly periodic wave solutions and other exact excitations are obtained by the use of a simple algebraic transformation relation between the generalized variable coefficient KdV equation and a generalized cubic nonlinear Klein－Gordon equation.

Key words: generalized variable coefficient KdV equation, general mapping approach, travelling wave solution

中图分类号:  (Solutions of wave equations: bound states)

  • 03.65.Ge
02.60.Lj (Ordinary and partial differential equations; boundary value problems) 02.30.Sa (Functional analysis)