Traveling wave solutions of a moderate amplitude shallow water wave model

Abstract:

The author studies the traveling wave solutions of a shallow water wave model with moderate amplitude by qualitative analysis methods of planar dynamical systems. Using the dynamical properties of the integrable systems, we discuss the bifurcation of its traveling wave system, from which we obtain the existence conditions of the bounded traveling solutions, including solitary wave solutions, periodic wave solutions, kink-like wave solutions and antikink-like wave solutions, and the exact expressions of these traveling wave solutions. Furthermore, we simulate these solutions by the Maple 18 software to verify our results.

Key words:Planar dynamical systems; Traveling wave solutions; Moderate amplitude; Periodic cusp wave solution; Numerical simulations