On the dynamics of exact solutions to a (3+1)-dimensional YTSF equation emerging in shallow sea waves: Lie symmetry analysis and generalized Kudryashov method

Abstract

This paper focuses on obtaining a large number of exact solutions to the highly nonlinear (3+1)-dimensional Yu–Toda–Sassa–Fukuyama (YTSF) equation, which is important in fluid dynamics, plasma physics, nonlinear sciences, and weakly dispersive media, among other things. The primary goal of this research is to obtain a variety of exact soliton solutions and different dynamical wave-forms of the YTSF equation using two different techniques: Lie symmetry and generalized Kudryashov (GK) methods. These techniques reduce the considered partial differential equation (PDE) into ordinary differential equations (ODEs). Hereafter, a variety of exact solutions are derived with the help of the associated subalgebras and wave transformation by the Lie symmetry technique and GK technique, respectively. The obtained exact solutions involve various arbitrary constants, parameters, and arbitrary functionals that enhance the dynamic representation of the derived solutions in the research area. We use numerical simulations to generate 3-dimensional graphics and contour plots to determine the dynamical behavior of the obtained exact solutions. The physical interpretation of interaction soliton solutions demonstrates a rich diversity of attained solutions, such as solitons, kink waves, kink wave interaction with solitons, and others.