摘要
研究了组合KdV型方程ut+aupux+bu2pux+uxxx=0(b≥0,p>0)孤波解的轨道稳定性.研究表明,组合KdV型方程孤波解的轨道稳定性不仅受最高次数非线性项bu2pux的影响,还受到另一非线性项aupux的影响.当b>0,0<p≤2时,该方程恒正的孤波解u1(x-ct)在a>0时轨道稳定,a<0时轨道不稳定;该方程恒负的孤波解u2(x-ct)在a<0时轨道稳定,a>0时轨道不稳定.指出了p=2,a>0时组合KdV型方程的孤波解具轨道稳定性的原因是方程中含系数a的这项具有促使稳定化的作用.
The orbital stability of solitary waves of compound KdV-type equation of the form ut＋aupux＋bu2pux＋uxxx=0 was studied,where b≥0,p0.The orbital stability of solitary waves was not only affected by the highest order non-linear term bu2pux,but also by the non-linear term aupux.As the paraments b0 and 0p≤2,the positive solitary wave u1（x-ct） is stable when a0,and unstable when a0;the stability of the negative solitary wave u2（x-ct） is contradiction.In particular,it is pointed out that the nonlinear term with coefficient a makes contributes to the stability of the solitary waves when p=2 and a0.
出处
《上海理工大学学报》
CAS
北大核心
2010年第2期103-109,共7页
Journal of University of Shanghai For Science and Technology
基金
上海市重点学科建设资助项目(S30501)
上海市自然科学基金资助项目(10ZR1420800)
关键词
轨道稳定
组合KDV方程
孤立波
谱分析
orbital stability
general compound KdV-type equation
solitary waves
spectral analysis
