具有分布时滞的奇异扰动KdV-KS方程的孤立波

Solitary Waves of Singularly Perturbed KdV-KS Equation with Distributed Delay

摘要: 我们研究一类基于KdV方程的非线性反应扩散方程，其非线性项具有分布时滞，高阶项是奇异扰动项，即著名的KS条件，我们称之为KdV-KS方程。我们主要研究孤立波的存在性，通过运用几何奇异摄动和线性链的技巧，证明了当平均时滞适当小时孤立波解的保持性，这里我们不需要原始KdV方程孤立波解的显式表达式。

Abstract: We study a sort of nonlinear reaction diffusion equation based on the Korteweg-de Vries (KdV) equation with a convolution term which introduces a time delay in the nonlinearity and with a higher order singularly perturbing term as the Kuramoto-Sivashinsky (KS) equation, called KdV-KS equation. We focus on the question of the existence of solitary wave solutions. By using geometric singular perturbation analysis and the linear chain trick, we prove that the solitary wave solutions persist when the average delay is suitably small. The explicit expression of original KdV solitary is not required.