(untitled) (European Journal of Pure and Applied Mathematics, 2025)
We study the nature of a (2+1)-dimensional nonlinear wave equation using the Lie symmetry analysis method. This problem is reduced to ordinary differential equations (ODEs) using non-similar subalgebras of Lie symmetries. We presented explicit solutions by solving the reduced ODEs. The conserved vectors were constructed using the Lagrange multiplier method. Using these conserved vectors, we also derived the exact solutions of the nonlinear wave equation. Consequently, 3D graphics were used to analyze and illustrate the graphical representations of the solutions.