Analytical solutions and conservation laws of a generalized (3+1)-dimensional nonlinear evolution equation appearing in mathematical physics

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematical Sciences, Sol Plaatje University, Private Bag X5008, Kimberly, 8300, Republic of South Africa.

2 Department of Mathematics, Faculty of Science, University of Botswana, Private Bag 22, Gaborone, Botswana.

3 Department of Mathematical Sciences, University of South Africa, UNISA 0003, Republic of South Africa.

Abstract

In mathematical physics, the study of solutions to nonlinear evolution equations has always been important, especially in the fields of nonlinear optics, fluid dynamics, and condensed matter physics. We study a generalized (3+1)-dimensional nonlinear evolution equation as a key consequence. This underlying equation is discovered to admit an endless number of conservation laws and point symmetries. Traveling wave solutions of physical interest are demonstrated by combining the Lie symmetry method with ansatz techniques. Furthermore, we use the multiplier approach to obtain the underlying equation's infinitely many conservation laws. It is predicted that these findings may be utilized to better understand how nonlinear waves propagate in a range of nonlinear physical systems, such as fluid mechanics and nonlinear optics. The solution dynamics are presented graphically.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 09 September 2025

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History

  • Receive Date: 02 November 2024
  • Revise Date: 09 May 2025
  • Accept Date: 08 September 2025

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