中国物理B ›› 2002, Vol. 11 ›› Issue (11): 1111-1114.doi: 10.1088/1009-1963/11/11/304

• GENERAL • 上一篇    下一篇

Mapping deformation method and its application to nonlinear equations

李画眉   

  1. The College of Mathematics, Physics and Information Science, Zhejiang Normal University, Jinhua 321004, China
  • 收稿日期:2002-04-14 修回日期:2002-06-11 出版日期:2005-06-12 发布日期:2005-06-12
  • 基金资助:
    Project supported by the Doctoral Programme Foundation of the Institutions of Higher Education of China (Grant No 2000024832).

Mapping deformation method and its application to nonlinear equations

Li Hua-Mei (李画眉)   

  1. The College of Mathematics, Physics and Information Science, Zhejiang Normal University, Jinhua 321004, China
  • Received:2002-04-14 Revised:2002-06-11 Online:2005-06-12 Published:2005-06-12
  • Supported by:
    Project supported by the Doctoral Programme Foundation of the Institutions of Higher Education of China (Grant No 2000024832).

PDF (PC)

524

赞

摘要： An extended mapping deformation method is proposed for finding new exact travelling wave solutions of nonlinear partial differential equations (PDEs). The key idea of this method is to take full advantage of the simple algebraic mapping relation between the solutions of the PDEs and those of the cubic nonlinear Klein－Gordon equation. This is applied to solve a system of variant Boussinesq equations. As a result, many explicit and exact solutions are obtained, including solitary wave solutions, periodic wave solutions, Jacobian elliptic function solutions and other exact solutions.

Abstract: An extended mapping deformation method is proposed for finding new exact travelling wave solutions of nonlinear partial differential equations (PDEs). The key idea of this method is to take full advantage of the simple algebraic mapping relation between the solutions of the PDEs and those of the cubic nonlinear Klein－Gordon equation. This is applied to solve a system of variant Boussinesq equations. As a result, many explicit and exact solutions are obtained, including solitary wave solutions, periodic wave solutions, Jacobian elliptic function solutions and other exact solutions.

Key words: variant Boussinesq equations, nonlinear Klein－Gordon equation, exact solution

中图分类号:  (Partial differential equations)

  • 02.30.Jr
02.10.-v (Logic, set theory, and algebra) 02.60.Lj (Ordinary and partial differential equations; boundary value problems)