Vol.4 No.6 (November 2014)
Solitary Waves of Singularly Perturbed KdV-KS Equation with Distributed Delay
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.
蒋永新 (2014) 具有分布时滞的奇异扰动KdV-KS方程的孤立波。 理论数学， 4， 251-260. doi: 10.12677/PM.2014.46037
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