New multi-soliton, Y-type, X-type, and interaction physical phenomena to a generalized breaking soliton system

Abstract

Based on the Hirota bilinear method, a generalized breaking soliton system is under investigation, which describes the interaction phenomena of the Riemann wave with a long wave through two spatial variables in nonlinear media. Some explicit exact solutions for a (3+1)-dimensional generalized breaking soliton system, including multi-soliton, Y-type, X-type, and multi-lump waves, and three structures of interaction solutions between them are explored. Also, the long-wave method is applied to N-soliton waves to derive M-lump waves. To illustrate their dynamic characteristics, 3-dimensional plots and contour plots are provided. We expect that the wave propagation presented in this research may be used to investigate exact wave solutions to other nonlinear integro-differential equations.