修正Camassa-Holm方程变式孤立波解的轨道不稳定性

Orbital Instability of Solitary Wave Solutions for a Variant of Modified Camassa-holm Equation

孤立波是非线性科学中的一个重要方面,而孤子现象又与孤立波的稳定性密切相关。为研究修正Camassa-Holm方程变式的一族显式孤立波解的轨道不稳定性质,采用了半群方法,并通过详细计算得到对初值问题解的衰减估计。结果表明:所研究的孤立波在波速c的稳定范围之外是轨道不稳定的。

Solitary wave is an very important part in nonlinear science. And the phenomenon of solitons is closely related to the stability of solitary waves. In order to study a set of explicit solitary waves for a variant of a modified Camassa-Holm （INCH） equation, the method of semi-group was used, and the decay estimate of the primitives of the solutions was obtained after detailed computation. The results showed that the waves are orbitally instable when the speed outsides the range of stability.