On traveling wave solutions: The Wu–Zhang system describing dispersive long waves

Abstract

In this paper, we construct exact families of traveling wave (periodic wave, solitary wave, shock wave, singular-wave, singular-periodic wave, and singular-solitary wave) solutions of a well-known system of nonlinear PDEs, the Wu–Zhang system, which describes (1[Formula: see text]+[Formula: see text]1)-dimensional dispersive long waves. This system is solved by using the generalized [Formula: see text] expansion method, where G satisfies the Jacobi elliptic equation of fourth order. Meanwhile, the mechanical features of some families are explained through three-dimensional figures.