Group Analysis of a Class of Nonlinear Wave Equations

Authors

  • M. Usman College of Electrical and Mechanical Engineering (CEME), National University of Sciences and Technology (NUST), H-12 Islamabad 44000, Pakistan
  • Akhtar Hussain Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan
  • M. Umar Farooq College of Electrical and Mechanical Engineering (CEME), National University of Sciences and Technology (NUST), H-12 Islamabad 44000, Pakistan
  • Jorge Herrera Facultad de Ciencias Naturales e Ingenieria, Universidad de Bogota Jorge Tadeo Lozano, Bogota 110311, Colombia

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i4.6128

Keywords:

Lie symmetries, conservation laws, invariant solutions, nonlinear wave equations

Abstract

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.

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Published

2025-11-05

Issue

Vol. 18 No. 4: (October 2025)

Section

Partial Differential Equations and Dynamical Systems

License

Copyright (c) 2025 M. Usman, Akhtar Hussain, M. Umar Farooq, Jorge Herrera

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How to Cite

Group Analysis of a Class of Nonlinear Wave Equations. (2025). European Journal of Pure and Applied Mathematics, 18(4), 6128. https://doi.org/10.29020/nybg.ejpam.v18i4.6128