We study the Wu-Zhang nonlinear evolution system of PDE which describes the propagation of \( (1+1) \) dimensional dispersive long waves on shallow water. It contains the elevation of the water u and the surface velocity v.We are looking for travelling wave solutions of the system that satisfy some system of ODE. It turns out that v equals a second order polynomial of u, while u is a solution of second order autonomous nonlinear ODE. u is written into integral form and can be found by inverse mapping theorem. The corresponding integral is expressed by Legendre functions of I, II and third kind. In some special cases u is written explicitly by elementary functions and in other ones it is a rational function of the Jacobi elliptic functions sn, cn.