Exploring Novel Solutions for the Generalized q-Deformed Wave Equation

Document Type : Research Paper

Authors

1 Department of Mathematics, Center of Basic Science, Misr University for Science and Technology, Giza 12511, Egypt.

2 Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, Egypt.

Abstract

Our primary goal is to address the $q$-deformed wave equation, which serves as a mathematical framework for characterizing physical systems with symmetries that have been violated. By incorporating a $q$-deformation parameter, this equation expands upon the traditional wave equation, introducing non-commutativity and non-linearity to the dynamics of the system. In our investigation, we explore three distinct approaches for solving the generalized $q$-deformed wave equation: the reduced $q$-differential transform method (R$q$DTM) \cite{1}, the separation method (SM), and the variational iteration method (VIM). The R$q$DTM is a modified version of the differential transform method specially designed to handle $q$-deformed equations. The SM aims to identify solutions that can be expressed as separable variables, while the VIM employs an iterative scheme to refine the solution. We conduct a comparative analysis of the accuracy and efficiency of the solutions obtained through these methods and present numerical results. This comparative analysis enables us to evaluate the strengths and weaknesses of each approach in effectively solving the $q$-deformed wave equation, providing valuable insights into their applicability and performance. Additionally, this paper introduces a generalization of the $q$-deformed wave equation, as previously proposed in \cite{2}, and investigates its solution using two different analytical methods: R$q$DTM, SM, and an approximation method known as VIM.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 30 April 2024

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History

  • Receive Date: 05 December 2023
  • Revise Date: 07 January 2024
  • Accept Date: 09 February 2024

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