Resonant Y-type soliton, X-type soliton and some novel hybrid interaction solutions to the (3+1)-dimensional nonlinear evolution equation for shallow-water waves

Abstract

This research aims to explore some novel solutions to the (3+1)-dimensional nonlinear evolution equation (NEE) for the shallow-water waves. The resonant Y-type soliton (YTS) and X-type soliton (XTS) solutions are derived by applying the novel resonant conditions on the N-soliton solutions(N-SSs) which are extracted via the Hirota bilinear approach. Additionally, some novel and interesting hybrid interaction solutions like the interaction between Y-type soliton and 1-soliton, interaction between Y-type soliton and 1-breather solution, interaction between the Y-type soliton and the soliton molecule on the (x, y)-plane, and interaction between the X-type soliton and 1-soliton are also ascertained. The dynamic attributes of the obtained solutions are described graphically to unveil their physical behaviors. The findings in this work can help us better apprehend the nonlinear dynamics of the considered equation.