sine-Gordon型方程的Jacobi椭圆函数精确解

J4 ›› 2009, Vol. 26 ›› Issue (3): 278-287.

sine-Gordon型方程的Jacobi椭圆函数精确解

套格图桑斯仁道尔吉

内蒙古师范大学数学科学学院, 内蒙古呼和浩特 010022

收稿日期:2008-06-13 修回日期:2008-07-28 出版日期:2009-05-28 发布日期:2009-05-07
作者简介:套格图桑（1964－），硕士，副教授，研究方向为孤立子与可积系统理论及其应用。
基金资助:
国家自然科学基金(10461006)、内蒙古自治区高等学校科学研究基金(NJZZ07031)、内蒙古自治区自然科学基金(200408020103)和内蒙古师范大学自然科学青年研究计划(QN005023)

Jacobi elliptic function exact solutions of sine-Gordon equation

TAOGeTuSang, SIRenDaoErJi

College of Mathematical Science, Inner Mongolia Normal University, Huhhot 010022, China

Received:2008-06-13 Revised:2008-07-28 Published:2009-05-28 Online:2009-05-07

摘要/Abstract

摘要：

本文给出一种三角函数型辅助方程及其它的解,并借助符号计算系统~Mathematica,把该方程直接应用到sine-Gordon方程、双sine-Gordon方程和MKdV-sine-Gordon方程,得到了Jacobi椭圆函数精确解以及退化后的孤波解和三角函数波解.

关键词: 三角函数型辅助方程, sine-Gordon型方程, Jacobi椭圆函数, 精确解

Abstract:

The auxiliary equation of the triangle function type and its solutions are given. The equation is directly applied to sine-Gordon equation, double sine-Gordon and mKdV sine-Gordon, with the help of symbolic computation system Mathematica, the Jacobi elliptic function exact solutions and degenerated solitary wave solutions and triangle function wave solutions of the equations are obtained.

Key words: auxiliary equation of triangle function type, sine-Gordon equation, Jacobi elliptic function, exact solution

中图分类号:

O175.29

套格图桑斯仁道尔吉. sine-Gordon型方程的Jacobi椭圆函数精确解[J]. J4, 2009, 26(3): 278-287.

TAOGeTuSang, SIRenDaoErJi. Jacobi elliptic function exact solutions of sine-Gordon equation[J]. J4, 2009, 26(3): 278-287.

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