New solitary wave and Multiple soliton solutions of (3 + 1)-dimensional KdV type equation by using Lie symmetry approach

TL;DR

This paper applies Lie symmetry methods to derive exact solitary wave and multi-soliton solutions of a (3+1)-dimensional KdV type equation, providing explicit analytic forms and graphical visualizations.

Contribution

It introduces a Lie symmetry approach to find and classify exact solutions of a higher-dimensional KdV type equation, including solitary and multi-soliton solutions.

Findings

Exact solutions in explicit form obtained

Solutions include travelling, kink, and multi-solitons

Graphical profiles illustrate solution behaviors

Abstract

Solitary waves are localized gravity waves that preserve their consistency and henceforth their visibility through properties of nonlinear hydrodynamics. Solitary waves have finite amplitude and spread with constant speed and constant shape. In this paper, we have used Lie group of transformation method to solve (3 + 1)-dimensional KdV type equation. We have obtained the infinitesimal generators, commutator table of Lie algebra for the KdV type equation. We have achieved a number of exact solutions of KdV type equation in the explicit form through similarity reduction. All the reported results are expressed in analytic (closed form) and figured out graphically through their evolution solution profiles. We characterized the physical explanation of the obtained solutions with the free choice of the particular parameters by plotting some 3D and 2D illustrations. The geometrical analysis explains that the nature of solutions is travelling wave, kink wave, single solitons, doubly solitons and curve-shaped multisolitons.