A new class of nonlinear superposition between lump waves and other waves for Kadomtsev–Petviashvili I equation

Abstract

In most cases, the lump wave will collide with line waves and breather waves in the hybrid solutions for (2 + 1)-dimensional integrable systems. However, this study introduces a new constraint condition to construct a nonlinear superposition in which the lump wave does not collide with other waves forever. In particular, the soliton molecule consisting of a lump wave, a line wave and any number of breather waves is derived for the first time by the continued introduction of velocity resonance. The new constraints mentioned in this paper will break the traditional understanding of the interaction between a lump and other waves. And this method can be extended to other (2 + 1)-dimensional integrable systems.