Multiple soliton, M-lump and interaction solutions to the (3+1)-dimensional soliton equation

Abstract

One of the most effective ways to understand nonlinear quantum systems is with lump solutions. The objective of this study is to acquire more about the (3+1)-dimensional soliton equation. We successfully present this equation with various solitons and M-lump solutions. We adopt specific parameter values to accentuate the physical features of the provided exact solutions through 3D and contour plots as doing so is of extreme significance. The submitted results indicate the physical qualities of lump-and-lump interaction events in various nonlinear physical processes.