On the dynamics of the nonautonomous multi-soliton, multi-lump waves and their collision phenomena to a (3+1)-dimensional nonlinear model

Abstract

One of the most popular ways to solve wave equations and explain nonlinear physical phenomena is with nonautonomous soliton solutions. This work aims to analyze the (3+1)-dimensional variable-coefficient Kudryashov–Sinelshchikov model, which explains pressure waves in liquid with flocs. Fluid dynamics, a subfield of fluid mechanics used in physics and engineering, is the study of how liquids and gases flow. There are many subfields within it, including aerodynamics and hydrodynamics. There are several uses for fluid dynamics, namely quantifying forces and moments. Using Hirota direct method, we auspiciously provide multiple solitons and M-lump solutions to this equation. We use specified input variables to accentuate the physical traits of the results obtained via two-, three-dimensional, and contour graphics since doing so is significant. The findings are applied to exemplify the physical traits of lump solutions and the collision-related elements of various nonlinear physical processes.