Line solitons, lumps, and lump chains in the (2+1)-dimensional generalization of the 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 the hybrid solution comprising one lump soliton and an arbitrary number of line solitons or/and lump chains is derived through the introduction of a long wave 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.

Keywords

• Long wave limit
• Soliton molecule
• Velocity resonance
• Collision