中国物理B ›› 2007, Vol. 16 ›› Issue (7): 1848-1854.doi: 10.1088/1009-1963/16/7/007

• GENERAL • 上一篇    下一篇

The projective Riccati equation expansion method and variable separation solutions for the nonlinear physical differential equation in physics

马正义   

  1. College of Mathematics and Physics, Zhejiang Lishui University, Lishui 323000, China
  • 收稿日期:2007-02-06 修回日期:2007-02-23 出版日期:2007-07-04 发布日期:2007-07-04
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10272071), the Natural Science Foundation of Zhejiang Province, China (Grant No Y606049) and the Key Academic Discipline of Zhejiang Province, China (Grant No 200412).

The projective Riccati equation expansion method and variable separation solutions for the nonlinear physical differential equation in physics

Ma Zheng-Yi(马正义)†   

  1. College of Mathematics and Physics, Zhejiang Lishui University, Lishui 323000, China
  • Received:2007-02-06 Revised:2007-02-23 Online:2007-07-04 Published:2007-07-04
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10272071), the Natural Science Foundation of Zhejiang Province, China (Grant No Y606049) and the Key Academic Discipline of Zhejiang Province, China (Grant No 200412).

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摘要： Using the projective Riccati equation expansion (PREE) method, new families of variable separation solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) with arbitrary functions for two nonlinear physical models are obtained. Based on one of the variable separation solutions and by choosing appropriate functions, new types of interactions between the multi-valued and single-valued solitons, such as a peakon-like semi-foldon and a peakon, a compacton-like semi-foldon and a compacton, are investigated.

Abstract: Using the projective Riccati equation expansion (PREE) method, new families of variable separation solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) with arbitrary functions for two nonlinear physical models are obtained. Based on one of the variable separation solutions and by choosing appropriate functions, new types of interactions between the multi-valued and single-valued solitons, such as a peakon-like semi-foldon and a peakon, a compacton-like semi-foldon and a compacton, are investigated.

Key words: projective Riccati equation, nonlinear physical equation, variable separation solution, soliton

中图分类号:  (Solitons)

  • 05.45.Yv
02.30.-f (Function theory, analysis)