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

摘要

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 KleinGordon 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.%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.