No abstract

Soliton molecules may exists in both experimental and theotetical aspects. In this work, we investigate the (2+1)-dimensional B-type Kadomtsev–Petviashvili equation, which can be used to describe weakly dispersive waves propagating in the quasi media and fluid mechanics. Soliton molecules are generated by N-soliton solution and a new velocity resonance condition. Furthermore, soliton molecules can become to asymmetric solitons when the distance between two solitons of the molecule is small enough. Based on the N-soliton solution, we obtain some novel interaction solutions which component of soliton molecules, breather waves and lump waves by deal with part of parameters by applying velocity resonance, module resonance and long wave limit method, and the interactions are elastic. Finally, some graphic analysis are discussed to understand the propagation phenomena of these solutions.

No abstract

Based on the hybrid solutions to (2+1)-dimensional Kadomtsev–Petviashvili (KP) equation, the motion trajectory of the solutions to KP equation is further studied. We obtain trajectory equation of a single lump before and after collision with line, lump, and breather waves by approximating solutions of KP equation along some parallel orbits at infinity. We derive the mathematical expression of the phase change before and after the collision of a lump wave. At the same time, we give some collision plots to reveal the obvious phase change. Our method proposed to find the trajectory equation of a lump wave can be applied to other (2+1)-dimensional integrable equations. The results expand the understanding of lump, breather, and hybrid solutions in soliton theory.

Soliton molecules are firstly obtained by velocity resonance for the Gerdjikov–Ivanov equation, and n-order smooth positon solutions for the Gerdjikov–Ivanov equation are generated by means of the general determinant expression of n-soliton solution. The dynamics of the smooth positons of the Gerdjikov–Ivanov equation are discussed using the decomposition of the modulus square, the trajectories and time-dependent “phase shifts” of positons after the collision can be described approximately. Additionally, some novel hybrid solutions consisting solitons and positons are presented and their rather complicated dynamics are revealed.