标题： 关于Korteweg–de Vries型方程族中带有分数阶色散的行波稳定性 显示英文标题

标题： Stability of travelling waves to Korteweg--de Vries type equations with fractional dispersion

摘要： 我们研究了具有分数色散和整数指数双幂非线性项的Korteweg-de Vries型方程的行波解的稳定性。这类方程是否具有基态解可能取决于这两个指数的奇偶组合以及色散的强度。因此，我们从奇偶性和色散的角度观察行波解的稳定性现象，并对行波解的现象进行了分类。本文的重点是稳定行波解。 显示英文摘要

摘要： We study stability of travelling wave solutions to Korteweg--de Vries type equations which has the fractional dispersion and integer-indices double power nonlinearities. It may depend on parity combinations of the two indices and the strength of dispersion whether these equations have a ground state solution. Therefore, we observe the stability phenomena on travelling wave solutions from the perspective of the parities and the dispersion, and we give the classification of phenomena on travelling wave solutions. In this paper, we focus on stable travelling wave solutions.