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一个非线性行波方程孤立波解的存在性

夏良娟1 丁丹平2   

  1. 1.镇江高专，江苏 镇江 212001

    2.江苏大学 非线性科学研究中心,江苏 镇江 212013

  • 收稿日期:2006-06-30 修回日期:2007-03-23 出版日期:2007-07-30 发布日期:2007-07-30

Existence of Solitary Wave Solution to a Nonlinear Traving Wave Equation

XIA Liang-Juan1, DING Dan-ping 2   

  1. 1．Zhengjiang College, Zhenjiang 212001, China；
    2．Center of Nonlinear Science Reasearch,Jiangsu University,Zhenjiang 212013,China
  • Received:2006-06-30 Revised:2007-03-23 Online:2007-07-30 Published:2007-07-30

摘要： 该文研究一个非线性波动方程，提出求解波动方程孤立波存在性的有效方法。此方程是Kdv方程和MKdv方程的一个推广形式，本文利用一类平面自治系统同宿轨与孤立波之间的关系，通过分析的方法及动力系统分叉理论，研究了自治系统在各种参数条件下同宿轨的情况，进而研究了一个非线性波动方程孤立波的存在情况。

关键词: 波动方程, 孤立波, 同宿轨

Abstract: Non-linear traveling wave equation is studied,and a kind of effective methods for solitary waves solution to a non-linear traveling wave equation is presented,which is a generalized form of Kdv equation and Mkdv equation.We use the relation between homoclinic orbit and solitary waves of planar autonomous ,and study the homoclinic orbits of autonomous system with various parameters using the bifurcation theory of dynamical systems and an analytical method.Existence of solitary waves of the nonlinear traving wave equation is investigated.

Key words: traving wave equation, solitary wave, homoclinic orbit