Novel multiple localized wave solutions and soliton molecules for the (2+1)-dimensional Korteweg-de Vries equation

Abstract

This article focuses on the exploration of novel soliton molecules for the (2+1)-dimensional Korteweg-de Vries equation. Specifically, Hirota bilinear form is derived through Bell polynomial method, and a soliton molecule comprising one lump soliton and an arbitrary number of line solitons or/and breather solitons is derived through the introduction of a longwave limit and new constraint conditions between the parameters of the N-soliton solutions and velocity resonance. The paper presents both analytical and graphical demonstrations of a range of interactions, showcasing the propagation of nonlinear localized waves. The findings of this study could contribute to a better understanding of physical phenomena associated with the propagation of nonlinear localized waves.