Resonance [formula omitted]-type soliton and hybrid solutions of a (2+1)-dimensional asymmetrical Nizhnik–Novikov–Veselov equation

Abstract

In this paper, a (2+1)-dimensional asymmetrical Nizhnik–Novikov–Veselov equation is studied. By adding some new constraints to the N-soliton solutions, the resonance Y-type soliton and the interaction solutions between M-resonance Y-type solitons and P-resonance Y-type solitons are obtained. The new types of solutions including the double openings of resonance Y-type soliton solutions and mixed solutions of resonance solitons and breathers are presented. The hybrid solutions consisting of the resonance Y-type solitons and the multiple lump waves are constructed by using restrictions and the long wave limit method. The trajectories of lump waves in hybrid waves are analyzed from the point of view of mathematical mechanism. The results are helpful to explain some new nonlinear phenomena in the theory of solitons.