New solutions for the generalized q-deformed wave equation with q-translation symmetry

Abstract

In this work, we explore the generalized discrete wave equation, which utilizes a specific irregular space interval. The introduction of this irregular space interval is motivated by its connection to the q-addition, a mathematical operation that arises in the nonextensive entropy theory. By taking the continuous limit, we obtain the wave equation with q-deformation, which captures the effects of the q-addition. To solve the generalized q-deformed wave equation, we investigate three different methods: the separation method, the reduced differential transform method, and the finite difference method. These methods offer distinct approaches for finding solutions to the equation. By comparing the results obtained from each method, we can evaluate their effectiveness and identify their respective strengths and limitations in solving the generalized q-deformed wave equation. The solutions obtained from this newly defined equation have potential applications in modeling physical systems with violated symmetries. The inclusion of the q-deformation allows for a more comprehensive description of such systems, which may exhibit nonextensive behavior or possess irregularities in their spatial intervals. By incorporating these features into the wave equation, we can improve our understanding and modeling capabilities of complex physical phenomena.

Keywords

• q-calculus
• q-deformed
• q-translation
• separation method
• rdtm
• fdm