Propagation of lump-type waves in nonlinear shallow water wave.

In this work, a new extended shallow water wave equation in (3+1) dimensions was studied, which represents abundant physical meaning in a nonlinear shallow water wave. We discussed the interaction between a lump wave and a single solitary wave, which is an inelastic collision. Further, the interaction between a lump wave and two solitary waves and the interaction between a lump wave and a periodic wave was also studied using the Hirota bilinear method. Finally, the interaction among lump, periodic and one solitary wave was investigated. The dynamic properties of the obtained results are shown and analyzed by some three-dimensional images.