A new superposition between lump, breather and line waves of the (2+1)-dimensional generalized Korteweg–de Vries equation in fluid mechanics

Abstract

This paper focuses on a new superposition between a single lump wave, breather waves and line solitons of the [Formula: see text]-dimensional generalized Korteweg–de Vries (gKdV) equation. After deriving the N-soliton solutions, a new constraint, the long-wave limit and mode resonance method are used to construct a new hybrid solution. Further, a new velocity resonance condition is proposed to obtain a velocity resonance solution consisting of a single lump wave, a line soliton and breather waves, which remains relatively stationary and form a new bound state. It is worth pointing out that in most of the previous literature, lump wave and other waves will separate after they collide, but this paper derives a different result.