Persistence of Kink and Periodic Waves to Singularly Perturbed Two-Component Drinfel’d–Sokolov–Wilson System

Abstract

This paper concerns the persistence of kink and periodic waves to singularly perturbed two-component Drinfel’d-Sokolov-Wilson system. Geometric singular perturbation theory is first employed to reduce the high-dimensional system to the perturbed planar system. By perturbation analysis and Abelian integrals theory, we then are able to find the sufficient conditions about the wave speed to guarantee the existence of heteroclinic orbit and periodic orbits, which indicates the existence of kink and periodic waves. Furthermore, we also show that the limit wave speed $$c_0(k)$$ c 0 ( k ) is increasing.