Unraveling Symmetry Properties in a Three-Dimensional Nonlinear Evolution Model via the Lie Group Method

Authors

  • Akhtar Hussain Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan
  • M. Usman College of Electrical and Mechanical Engineering (CEME), National University of Sciences and Technology (NUST), H-12 Islamabad 44000, Pakistan
  • Ahmed M. Zidan Department of Mathematics, College of Science, King Khalid University, Abha 61413 Saudi Arabia
  • 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.v18i3.6012

Keywords:

Lie group method, evolution model, symmetry algebra, Jaulent-Miodek hierarchy, Conservation laws

Abstract

This research focuses on a (3+1)-dimensional nonlinear evolution model originating from the Jaulent-Miodek hierarchy. Several tools can be used to examine the symmetry of the model. However, our primary emphasis lies in harnessing one of the most significant and powerful analytical tools available for this purpose: the Lie group method. The Lie group method is an effective approach for uncovering the symmetry properties inherent in a model and exploring group-invariant solutions using symmetry algebra. In addition, we applied Ibragimov's method to study conservation laws relevant to the considered model. Our study is significant as it contributes to the investigation of this model and addresses a particular gap in the group-theoretic approach in this context. Our findings represent novel contributions to the study of the model under consideration.

Author Biography

  • M. Usman, College of Electrical and Mechanical Engineering (CEME), National University of Sciences and Technology (NUST), H-12 Islamabad 44000, Pakistan

    Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan

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Published

2025-08-01

Issue

Vol. 18 No. 3: (July 2025)

Section

Mathematical Physics

License

Copyright (c) 2025 Akhtar Hussain, M. Usman, Ahmed M. Zidan, Jorge Herrera

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How to Cite

Unraveling Symmetry Properties in a Three-Dimensional Nonlinear Evolution Model via the Lie Group Method. (2025). European Journal of Pure and Applied Mathematics, 18(3), 6012. https://doi.org/10.29020/nybg.ejpam.v18i3.6012