mCH方程变式的一族显式孤立波解的稳定性

Stability of a Set of Explicit Solitary Wave Solutions for a Variant of a Modified Camassa-Holm Equation

在Grillakis,Shatah,Strauss建立的关于非线性哈密顿系统孤立波轨道稳定的抽象理论框架下,对修正的Camassa-Holm(mCH)方程的一个变式的一族显式孤立波解的轨道稳定性进行了研究。通过半群方法、谱方法以及详细的计算,验证了抽象理论的假设条件是成立的。从而证明了在波速c的某范围内孤立波解是轨道稳定的。

Based on the abstract result of orbital stability of solitary waves established by Grillakis, Shatah, and Strauss, orbital stability of a set of explicit solitary waves for a variant of a modified Camassa-Holm Equation is investigated. Using the methods of semi-group and spectral analysis, and after the detailed computation, it is verified that the assumptions in the abstract result are hold. Finally the waves are proved to be orbitally stable when the wave speed c lies in some range.