具任意次非线性项的非线性Klein-Gordon方程孤波解的轨道稳定性  

The Orbital Stability of Solitary Solutions to the Nonlinear Klein-Gordon Equation with Nonlinear Terms of any Degree

作　　者：刘小华[1,2] 张卫国[1] 

机构地区：[1]上海理工大学理学院,上海200093 [2]贵州民族学院理学院,贵阳550025

出　　处：《工程数学学报》2011年第3期375-379,共5页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11071164);上海市自然科学基金(10ZR1420800);上海市重点学科建设项目(S30501)~~

摘　　要：具任意次非线性项的非线性Klein-Gordon方程是一类非常重要的物理模型,它的孤波解的轨道稳定性有着很好的物理意义.本文利用抽象的Grillakis轨道稳定性理论和谱分析,讨论具任意次非线性项的非线性Klein-Gordon方程的孤波解的轨道稳定性.当非线性项的系数以及波速满足一定的条件时,得出了其钟状孤波解总是不稳定的,而扭状孤波解总是稳定的.从而揭示了非线性项的系数以及波速对孤波解的稳定性所起的作用.The nonlinear Klein-Gordon equation with nonlinear terms of any degree is a very important model in physics,the orbital stability of its solitary wave solutions has a very good physical implication.In this paper,the authors discuss the orbital stability of solitary wave solutions to the nonlinear Klein-Gordon equation with nonlinear terms of any degree,by applying the abstract results of Grillakis orbital theory and detailed spectral analysis.When the coefficients of nonlinear terms and the wave velocity satisfy some conditions,we obtain that its bell solitary wave solutions are unstable and the kink solitary wave solution is stable.So we show that the orbital stability of solitary wave solutions depends on the the coefficients of nonlinear terms and the wave velocity to some extent.

关 键 词：非线性KLEIN-GORDON方程 轨道稳定性 孤波解 非线性项 

分 类 号：O175.2[理学—数学]