Mixed Rational Lump-Solitary Wave Solutions to an Extended (2+1)-Dimensional KdV Equation

Abstract

Based on the bilinear method, rational lump and mixed lump-solitary wave solutions to an extended (2+1)-dimensional KdV equation are constructed through the different assumptions of the auxiliary function in the trilinear form. It is found that the rational lump decays algebraically in all directions in the space plane and its amplitude possesses one maximum and two minima. One kind of the mixed solution describes the interaction between one lump and one line solitary wave, which exhibits fission and fusion phenomena under the different parameters. The other kind of the mixed solution shows one lump interacting with two paralleled line solitary waves, in which the evolution of the lump gives rise to a two-dimensional rogue wave. This shows that these three interesting phenomena exist in the corresponding physical model.

Various nonlinear characteristics of breather/rogue waves and controllable interaction phenomena for a new KdV equation with variable coeffcients

“…where u = u(t, x, y), the subscripts represent the partial differential. Equation (1) can be described the ionacoustic waves in plasmas, shallow water waves in oceans, and pulse waves in large arteries [36]. If f (t), g(t), h(t), s(t) are constants, equation (1) is reduced to a (2+1)-dimensional KdV equation with constant coefficients [35], and the rational solutions, periodic cross-rational solutions, rational kink cross-solutions, M-lump solutions and homoclinic breather solutions for the KdV equation with constant coefficients are obtained [35][36][37][38][39].…”

“…Equation (1) can be described the ionacoustic waves in plasmas, shallow water waves in oceans, and pulse waves in large arteries [36]. If f (t), g(t), h(t), s(t) are constants, equation (1) is reduced to a (2+1)-dimensional KdV equation with constant coefficients [35], and the rational solutions, periodic cross-rational solutions, rational kink cross-solutions, M-lump solutions and homoclinic breather solutions for the KdV equation with constant coefficients are obtained [35][36][37][38][39]. But there are few researches about equation (1), some exact wave solutions, M-lump solutions and interaction phenomena of equation (1) are investigated, seen in [40,41].…”