非线性色散系统孤波解的轨道稳定性  

The Orbital Stability of the Solitary Solutions to the Nonlinear Dispersion System

作　　者：刘小华[1] 胡丽金 余孝军[2] 

机构地区：[1]贵州民族大学理学院,贵州贵阳550025 [2]贵州财经大学数学与统计学院,贵州贵阳550025

出　　处：《四川师范大学学报（自然科学版）》2016年第1期51-58,共8页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(71161005);贵州省科学技术基金([2013]2138);贵州省教育厅优秀科技创新人才支撑计划(KY[2012]092);贵州省教育厅"数学建模及其应用创新人才团队"基金(黔教科研发[2013]405号)

摘　　要：利用变分法考虑非线性色散系统孤波解的存在性.借助轨道稳定性抽象理论,构造泛函极值问题和哈密尔顿算子,并对算子进行谱分析,证明非线性色散系统孤波解的轨道稳定性取决于判别式的符号,并推广了已有文献的一些结论.In this paper,we investigate the existence of solitary wave solutions for the nonlinear dispersion system. By constructing the functional extremum problem and Hamilton operator,using spectral analysis and the orbital stability theory presented by Grillakis et al,we show that the solitary wave solutions of the the nonlinear dispersion system are orbitally stable or unstability as determined by the sign of a discriminant. The conclusions presented by the previous authors,such as Alarcon,Angulo and Motenegro,can be considered as special cases of our results.

关 键 词：孤波解 轨道稳定性 变分法 

分 类 号：O175.2[理学—数学]