Lump solutions and interaction behaviors to the (2+1)-dimensional extended shallow water wave equation

Abstract

In this paper, the exact solutions to the (2[Formula: see text]+[Formula: see text]1)-dimensional extended shallow water wave (SWW) equation are investigated by using its bilinear form and ansatz techniques. Following the method given by Ma [Phys. Lett. A 379 (2015) 1975–1978], two classes of lump solutions are constructed by searching for positive quadratic function solutions to the associated bilinear equation. Furthermore, two kinds of interaction solutions between a lump and solitary waves are presented by taking the solution of the associated bilinear equation as a linear combination function of a quadratic function and the double exponential function, one of which is the interaction solution between a lump and an exponentially decayed soliton, and the other one is the interaction solution between a lump and an exponentially decayed twin soliton. Finally, some figures are given to illustrate the dynamic properties of these obtained solutions.