Traveling waves of delayed Zakharov-Kuznetsov Kuramoto-Sivashinsky equation

Abstract

This paper deals with the existence of periodic wave and solitary wave solutions for the Zakharov-Kuznetsov equation with different perturbations. Firstly, we prove the existence of periodic wave and solitary wave solutions for the original Zakharov-Kuznetsov equation by means of the phase space analysis. Then we discuss the existence of periodic wave and solitary wave solutions for the Zakharov-Kuznetsov Kuramoto-Sivashinsky equation by combining the geometric singular perturbation theory and the Abelian integrals. It is also proved that the wave speed c0(h) is decreasing on h, and the upper and lower bounds of the limit wave speed are presented. Finally, the persistence of solitary wave solutions for delayed Zakharov-Kuznetsov Kuramoto-Sivashinsky equation is established by applying the geometric singular perturbation theory and the Melnikov method.