Lump wave solutions, lump-stripe soliton inelastic collision phenomena and rogue-type wave solutions for a generalized breaking soliton system in (3+1)-dimensions

Abstract

Based on five types of structures of the functional multi-layer neural network model, some explicit exact solutions for a (3+1)-dimensional generalized breaking soliton system including lump waves, lump-stripe solitons and rogue-type waves are explored by using bilinear neural network method without the datasets training. The 3-dimensional plots, 2-dimensional curves and density plots of these results obtained are provided to display their dynamic characteristics. In particular, the complete processes of lump wave and stripe soliton fusion phenomena are presented. We hope the formulations established in this paper could be applied to study the exact traveling wave solutions of other integrable nonlinear evolution equations.