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

Under investigation is a (3+1)-dimensional generalized breaking soliton equation in nonlinear media. The interaction solution between lump wave and N-soliton (N = 2,3,4) are derived. The interaction solution between lump wave and periodic waves is also studied. Breather-wave and multi-wave solutions are obtained. The dynamical behavior is demonstrated by some 3D graphics and density plots. By means of mathematical induction, we also obtain the exact solution containing three arbitrary functions.