Approximate symmetries of the perturbed KdV-KS equation

Articles in Press

Document Type : Research Article

Authors

• Akram Mohammadpouri ¹
• Mir Sajjad Hashemi ²
• Roya Abbasi ¹
• Rana Abbasi ¹

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

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

10.22067/ijnao.2025.90854.1551

Abstract

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.

Keywords

• Approximate Lie symmetries
• Commutator table
• Adjoint representation
• Reductions

Main Subjects

• Numerical methods for differential equations and its applications

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