Resonant Y-Type solutions, N-Lump waves, and hybrid solutions to a Ma-type model: a study of lump wave trajectories in superposition

Abstract

In this paper, we incorporate new constrained conditions into N-soliton solutions for a (2+1)-dimensional fourth-order nonlinear equation recently developed by Ma, resulting in the derivation of resonant Y-type solitons, lump waves, soliton lines and breather waves. We utilize the velocity-module resonance method to mix resonant waves with line waves and breather solutions.
To investigate the interaction between higher-order lumps and resonant waves, soliton lines, and breather waves, we use the long wave limit method. We analyze the motion trajectory equations before and after the collision of lumps and other waves.
To illustrate the physical behavior of these solutions, several figures are included. We also analyse the Painlev'{e} integrability as well as the existence of multi-soliton solutions for the Ma equation in general and show that our specific equation of Ma type is not Painlev'{e} integrable, nevertheless it has multi-soliton solution.