Self-Similar Solutions to the Lin-Reissner-Tsien Equation via the Power Index Method

Authors

  • Zeshan Haider Department of Mathematics, Faculty of Basic and Appied Sciences, Air University, PAF Complex E-9, Islamabad 44000, Pakistan
  • Khalil Ahmad Department of Mathematics, Faculty of Basic and Appied Sciences, Air University, PAF Complex E-9, Islamabad 44000, Pakistan
  • Muhammad Shoaib Arif Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
  • Ateeq Ur Rehman Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
  • Muhammad Noman Qureshi Department of Mathematics, Faculty of Basic and Applied Sciences, Air University, PAF Complex E-9, Islamabad 44000, Pakistan

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i3.6248

Keywords:

Lin-Reissner-Tsien equation; power index method; self-similar transformation; self-similar solutions; nonlinear partial differential equations.

Abstract

In this paper, the (2 + 1)-dimensional Lin–Reissner–Tsien (LRT) equation is investigated using the Power Index Method (PIM). A self-similar transformation is applied to reduce the given partial differential equation (PDE) into an ordinary differential equation (ODE) through a change of variables based on scaling symmetry. The analytic solution of the resulting ODE is obtained using the symbolic computation software Maple 18 and basic techniques. The self-similar solutions of the LRT equation are then derived by combining the ODE solution with the self-similar transformation. The proposed method is effectively applied to generate new self-similar solutions of the LRT equation. Finally, graphical representations of all the obtained solutions are presented as 3D plots generated using Maple 18.

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Published

2025-08-01

Issue

Vol. 18 No. 3: (July 2025)

Section

Nonlinear Analysis

License

Copyright (c) 2025 Zeshan Haider, Khalil Ahmad, Muhammad Shoaib Arif, Ateeq Ur Rehman, Muhammad Noman Qureshi

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How to Cite

Self-Similar Solutions to the Lin-Reissner-Tsien Equation via the Power Index Method. (2025). European Journal of Pure and Applied Mathematics, 18(3), 6248. https://doi.org/10.29020/nybg.ejpam.v18i3.6248