Conservation Laws, Symmetry Reduction and Solutions for the 2D Nonlinear Wave Equation

This article delves into the exploration of the 2D nonlinear wave equation through a variety of adaptable methodologies. First, we employ the Lie point symmetry approach to identify all Lie symmetry generators for the equation. Subsequently, utilizing these generators, we reduce the dimensionality of the equation, resulting in ordinary differential equations. Additionally, we employ the unified Riccati method to generate soliton solutions for the traveling wave. This includes a range of kink solitons and other solitons characterized by hyperbolic functions. To elucidate the practical significance of these theoretical findings, we visually represent some of the solutions through 3D, contour, and 2D graphs, employing relevant physical parameters. The comprehensive outcomes are documented, serving as valuable resources for future investigations into the equation. These results underscore the efficacy of the applied techniques in analyzing other nonlinear physical phenomena spanning diverse disciplines within the realm of science and physics.