Solitary waves of singularly perturbed generalized KdV equation with high order nonlinearity

Abstract

<p style='text-indent:20px;'>The paper is concerned on solitary waves for singularly perturbed generalized KdV equation with high order nonlinear terms. We firstly give the phase portraits of system related to the unperturbed equation under various cases by theory of planar dynamical system. Then by using geometric singular perturbation theory and Melnikov's method, the existence of solitary wave solutions of generalized KdV equations with high order nonlinear terms is established. It is proven that some solitary wave solutions with particular wave speeds will persist under small perturbations.</p>