数学物理学报 ›› 2005, Vol. 25 ›› Issue (7): 956-964.

• 论文 • 上一篇    下一篇

广义射影Riccati方程方法与(2+1)维色散长波方程新的精确行波解

 智红燕, 陈勇, 张鸿庆   

  1. 大连理工大学应用数学系 大连 |116024 宁波大学数学系 宁波 |315211 中国科学院数学机械化重点实验室 北京 |100080
  • 出版日期:2005-12-30 发布日期:2005-12-30
  • 基金资助:

    国家自然科学基金(10072013)和国家重点基础研究发展规划项目(G1998030600)以及中国博士后基金、浙江省自然科学基金(Y604056)资助

Projective Riccati Equation Method and New Exact Travelling Wave Solutions for the (2+1)-dimensional Long Wave Equations

 ZHI Hong-Yan, CHEN Yong, ZHANG Hong-Qing   

  • Online:2005-12-30 Published:2005-12-30
  • Supported by:

    国家自然科学基金(10072013)和国家重点基础研究发展规划项目(G1998030600)以及中国博士后基金、浙江省自然科学基金(Y604056)资助

摘要:

助于符号计算软件Maple,通过一种构造非线性偏微分方程更一般形式行波解的直接方法,即改进的广义射影Ricccati方程方法, 求解(2+1)维色散长波方程,
得到该方程的新的更一般形式的行波解, 包括扭状孤波解, 钟状解,孤子解和周期解. 并对部分新形式孤波解画图示意.

关键词: 广义射影Riccati方程方法, (2+1)维色散长波方程, 行波解

Abstract:

Based upon a generally projective Riccati equation method, which is a direct and unified algebraic method for constructing more general form travelling wave solutions of nonlinear partial differential equations (PDEs) and implemented in a computer algebraic system, the authors  consider the (2+1)-dimensional dispersive long wave equations(DLWE). More and new general form solutions are obtained, including kink-shaped solitons,
bell-shaped solitons, singular solitons and periodic solutions.The properties of some new formal solitary wave solutions are shown by some figures.

Key words: Projective Riccati equation method, (2+1)-dimensional long wave equations (DLWE), Exact solution.

中图分类号: 

  • 35Q20