Dynamical Behavior of the Traveling Wave Solutions for a Modified Serre–Green–Naghdi System

In this paper, we investigate the dynamical behavior of the traveling wave system of the modified Serre–Green–Naghdi equations. The model equations can be considered as perturbed Serre–Green–Naghdi equations. It is shown that under a given parameter condition, the unperturbed system has two smooth periodic solution families and two smooth solitary wave solutions. When the small parameter [Formula: see text] the modified Serre–Green–Naghdi equations have no periodic wave solution and solitary wave solution.