Nonlinear superposition between lump soliton and other nonlinear localized waves for the (2+1)-dimensional Korteweg–de Vries–Sawada–Kotera–Ramani equation

Abstract

In the previous studies, the authors have reported the lump soliton collided with other nonlinear localized waves for (2+1)-dimensional Korteweg–de Vries–Sawada-Kotera–Ramani equation. However, this work will introduce a novel restrictive condition to reveal the nonlinear superposition between a lump soliton and other nonlinear localized waves. Under the premise of the acquired N-soliton solutions, the nonlinear superposition structures among lump soliton, stripe solitons, resonance Y-type solitons and breather waves guarantee that the lump soliton does not collide with other localized waves by means of the long wave limit approach, soliton resonance method and symbolic computation. Meanwhile, a variety of soliton molecules are yielded through nonlinear superposition and velocity resonance mechanisms. The obtained solutions in this work will bring about new perception of the interaction behavior between lump soliton and other nonlinear localized waves, and provide more brand new insights into the nonlinear phenomena triggered by the areas of plasma physics, fluid dynamics and nonlinear optics.