Persistence of solitary wave solutions to a singularly perturbed generalized mKdV equation

Abstract

The existence of solitary wave solutions for a perturbed generalized mKdV equation with a cubic evolution term is investigated. All possible solitary waves for the corresponding unperturbed equation are firstly explored by dynamical system analysis. Then by using geometric singular perturbation theory and Melnikov’s method, we prove that two solitary wave solutions of the unperturbed generalized mKdV equation with particularly chosen wave speeds will persist under small singular perturbation. The results of numerical simulations are consistent with our theoretical analysis.