Solitary wave and periodic wave for a generalized Nizhnik-Novikov-Veselov equation with diffusion term

Abstract

This paper is concerned with a generalized Nizhnik-Novikov-Veselov equation with weak backward diffusion term. The existence of solitary wave and periodic wave solutions are obtained by using the method of the dynamical system, especially the geometric singular perturbation theory and invariant manifold theory. Furthermore, based on the ratio of the Abelian integral, the monotonicity of the wave speed is established. At the same time, the bounds of the limit wave speed and the properties of the periodic wave solutions to this equation are also given.