J4 ›› 2009, Vol. 26 ›› Issue (6): 654-657.

• 量子物理 • 上一篇    下一篇

Camassa-Holm方程的等价变换

邱燕红 田宝单   

  1. 西南科技大学理学院 四川 绵阳 621010
  • 发布日期:2009-11-03
  • 通讯作者: 邱燕红(1981-),女,福建武夷山人,讲师,理学硕士,主要从事非线性数学物理及群论的研究。 E-mail:qyanhong318@163.com
  • 基金资助:

    四川省教育厅科研基金项目(07ZC053)

Equivalence transformation for the Camassa-Holm equation

QIU Yan-Hong, TIAN Bao-Dan   

  1. School of science, Southwest University of Science and Technology, Mianyang 621010,China
  • Online:2009-11-03

摘要:

利用改进的直接方法得到了一类Camassa-Holm方程的等价变换和对称群定理,建立了方程新解与旧解之间的关系,最后在已有的一些精确解的基础上利用对称群定理得到了Camassa-Holm方程的许多新的显式精确解。

关键词: 数学物理, 等价变换, 直接方法, Camassa-Holm方程, 精确解

Abstract:

A simple improved direct method is presented to find equivalence transforma- tion for a class of Camassa-Holm equation. Applying this equivalence transformation, the theorem of symmetry group for the Camassa-Holm equation is obtained, which describes the relationship between the new solutions and the old ones. Finally, some new exact and explicit solutions of the Camassa-Holm equation are obtained by the present references.

Key words: mathematical physics, equivalence transformation, direct method, Camassa- Holm equation, explicit solutions