Modified (2+1)-dimensional displacement shallow water wave system: Symmetries and exact solutions

A (2+1)-dimensional displacement shallow water wave system for perfect fluid has been constructed, recently. The displacement system was modified and the term related to the fluid viscosity was added to the model by means of dimensional analysis in this paper. For ideal fluids, the modified displacement system will degenerate to displacement system. Meanwhile, we studied the symmetries and similarity solutions of the modified displacement system. Calculation shows the modified displacement system is invariant under some Galilean transformations and space–time translations. Furthermore, some exact solutions of the newly proposed model are demonstrated with the help of the symmetry properties, and the exact solutions clearly show the role of fluid viscosity.