Symmetry reduced and exact non-traveling wave solutions of the (2+1)-D GSWW equation

In this paper, the (2+1)-dimensional generalized shallow water wave equation (GSWW) is reduced to a (1+1)-dimensional PDE with constant coefficients by means of the group method. Moreover, we determine some new exact non-traveling solutions with arbitrary function of the GSWW equation by means of the homoclinic test technique, Hirota method and auxiliary equation method, etc.