Dynamical solitary interactions between lump waves and different forms ofn-solitons (n→∞) for the (2+1)-dimensional shallow water wave equation

Abstract

We construct lump wave solution by using parametric limit approach from an interaction of double soliton solutions to the (2+1)-dimensional shallow water wave equation. We introduce new lemmas, theorems and corollaries with proofs and their dynamical interaction properties between lump waves and different forms of n-soliton solutions (n→∞). Besides, a number of examples of the theories are presented by choosing different types of interactions among lump, solitons and periodic waves. Finally, we display the dynamical collisions of the solutions to reflect the evolutions and flow directions in 3D and contour profiles of the model.