Approximate symmetries of the perturbed KdV-KS equation

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 13 بهمن 1403

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2025.90854.1551

نویسندگان

Akram Mohammadpouri^{* 1}؛ Mir Sajjad Hashemi²؛ Roya Abbasi¹؛ Rana Abbasi¹

¹Faculty of Mathematics, Statistics and Computer Sciences, University of Tabriz, Tabriz, Iran.

²Department of Mathematics, Basic Science Faculty, University of Bonab, Bonab, Iran

چکیده

The analysis of approximate symmetries in perturbed nonlinear partial differential equations stands as a cornerstone for unraveling complex physical behaviors and solution patterns. This paper delves into the investigation of approximate symmetries inherent in the perturbed KdV-KS equation, fundamental models in the realm of fluid dynamics, and wave phenomena. Our study commences by detailing the method to derive approximate vector Lie symmetry generators that underpin the approximate symmetries of the perturbed KdV-KS equation. These generators, while not exact, provide invaluable insights into the equation’s dynamics and solution characteristics under perturbations. A comprehensive approximate commutator table is subsequently constructed, elucidating the relationships and interplay between these approximate symmetries and shedding light on their algebraic structure. Leveraging the power of the adjoint representation, we examine the stability of these approximate symmetries when subjected to perturbations. Furthermore, we harness the concept of approximate symmetry reductions, a pioneering technique that allows us to distill crucial dynamics from the complexity of the perturbed equation. Through this methodology, we uncover invariant solutions and reduced equations that serve as effective surrogates for the original system, capturing its essential behavior and facilitating analytical and numerical investigations. In summary, our exploration into the approximate symmetries of the perturbed KdV-KS equation not only advances our comprehension of the equation’s intricate dynamics but also offers a comprehensive framework for studying the impact of perturbations on approximate symmetries, all while opening new avenues for tackling nonlinear PDEs in diverse scientific disciplines.

کلیدواژه‌ها

Approximate Lie symmetries؛ Commutator table؛ Adjoint representation؛ Reductions