Nonlinear superposition between lump waves and other waves of the (2 + 1)-dimensional asymmetrical Nizhnik–Novikov–Veselov equation

Abstract

The main attention of this paper is to study the nonlinear superposition between a lump wave and other types of localized waves of the (2 $+$ 1)-dimensional asymmetrical Nizhnik–Novikov–Veselov equation from an incompressible fluid. The hybrid solutions consisting of the lump waves, breather waves and line solitons are obtained with the aid of partial long wave limit method, in which the lump waves do not collide with or always sit on the other waves. A new nonlinear superposition between a lump wave and a resonance Y-type soliton is derived. Furthermore, the bound state among a lump wave, breather waves and line solitons, namely molecules, is obtained by means of introducing the new constraint conditions among the parameters of the N-soliton solutions and velocity resonance. The obtained various kinds of solutions are useful in analyzing the nonlinear superposition among the nonlinear localized waves and providing some meaningful results to explain the nonlinear phenomena arising in the fields of ocean waves, fluid mechanics and nonlinear optics.