Geometric singular perturbation method to the existence and asymptotic behavior of traveling waves for a generalized Burgers-KdV equation

摘要

In this paper, we discuss the existence and asymptotic behavior of traveling waves for a generalized Burgers-KdV equation. We show the heteroclinic orbits of the associated ordinary differential equations for the generalized Burgers-KdV equation with a special convolution kernel and then establish the existence result of traveling wave solutions for the Burgers-KdV equation by employing geometric singular perturbation theory and the linear chain trick. And the asymptotic behavior of traveling waves is obtained by using the standard asymptotic theory.