两非线性波方程真圈解的存在性和破缺性质

李继彬

doi:10.3879/j.issn.1000-0887.2009.05.001

两非线性波方程真圈解的存在性和破缺性质

doi: 10.3879/j.issn.1000-0887.2009.05.001

李继彬^1,2

浙江师范大学数学系,浙江金华 321004;2.昆明理工大学理学院,昆明 650093

基金项目: 国家自然科学基金资助项目(10671179,10831003)

详细信息

作者简介:
李继彬(1943- ),男,云南人,教授,博士生导师(Tel:+86-871-5171274;E-mail:jibinli@gmail.com).

中图分类号: O357.1
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- 被引次数: 0
出版历程
- 收稿日期: 2008-08-06
- 修回日期: 2009-03-20
- 刊出日期: 2009-05-15

Existence and Breaking Property of Real Loop-Solutions of Two Nonlinear Wave Equations

LI Ji-bin^1,2

Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China;

摘要

摘要: 对于某些非线性波方程,动力系统方法的分析说明所谓的圈孤子解和反圈孤子解实际上是人为的现象．所谓的圈孤子解由3个解合成,不是1个真解．是否存在非线性波方程,使得该方程的行波系统存在真正的1个圈解? 若这样的解存在,它们有怎样的精确参数表示?该文回答这些问题．
- 破缺波解 /
- 精确圈解 /
- 非线性波方程 /
- 平面动力系统
Abstract: Dynamical analysis revealed that for some nonlinear wave equations, loop-and inverted loop-soliton solutions are merely visual artifacts. So called loop-soliton solution consists of three solutions which is not one real solution. Whether or not there exist some nonlinear wave equations for which there exists a/real0 loop-solution? If yes, what are their precise parametric representations of these loop traveling wave solutions? These problems are answered.
- breaking wave solution /
- loop-solution /
- no nlinear wave equation /
- planar dynamical system

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参考文献(12)

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