Resonant multi-soliton solutions to the (2 + 1)-dimensional Sawada–Kotera equations via the simplified form of the linear superposition principle

Abstract

In this work, a simplified form of the linear superposition principle is proposed to facilitate the computational work and make the resonant multi-soliton solutions easily generated. The (2 + 1)-dimensional Sawada–Kotera (SK) equation, one of fifth-order KdV-like equations describing the nonlinear wave phenomena in shallow water, ion-acoustic waves in plasmas, etc., is investigated. Moreover, in order to demonstrate the power of the proposed method, a new version of the SK equation is further considered and examined. The general forms of resonant multi-soliton solutions are formally established. Furthermore, by taking about reverse engineering of the generated solutions, various versions of the (2 + 1)-dimensional SK equation can be derived that may make great contributions to real physical phenomena and enrich the related nonlinear sciences. Finally, the propagations of two- and three-soliton waves are presented.