New soliton structure and trajectory equation for the asymmetrical Nizhnik- Novikov-Veselov equation with variable coefficients in incompressible fluid

Abstract This paper focuses on some new soliton structures and dynamic properties of the (2+1)-dimensional asymmetrical Nizhnik-Novikov-Veselov equation with variable coefficients, which can be used to describe the nonlinear wave phenomena in incompressible fluid, such as parameter regulation of soliton structures, hybridization behavior between different solitons and trajectory equations of soliton collisions. Firstly, the N -soliton solutions and parameter regulations are studied based on the bilinear form of equations. Secondly, the M -order lump solutions and trajectory equations are discussed by employing the long wave limit method. Finally, we focused on studying the interaction behavior between different solitons and the trajectory equations before and after collision, and provided a proof of the trajectory between the lump solution and the n -soliton before and after collision (where n is any positive integer).