Lie Symmetry Analysis of Fractional Kersten–Krasil’shchik Coupled KdV–mKdV System

This paper investigates the invariance properties of the fractional Kersten–Krasil’shchik coupled KdV–mKdV system. By extending Lie symmetry analysis method to a fractional system, two vector fields are derived. The similarity transformation elegantly reduces the fractional system to a set of ordina...

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Bibliographic Details
Published in:Qualitative theory of dynamical systems 2025-02, Vol.24 (1), Article 17
Main Authors: Wang, Panpan, Feng, Xiufang, He, Shangqin
Format: Article
Language:English
Subjects:
Conservation laws
Difference and Functional Equations
Differential equations
Dynamical Systems and Ergodic Theory
Fields (mathematics)
Mathematics
Mathematics and Statistics
Power series
Symmetry
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Summary:This paper investigates the invariance properties of the fractional Kersten–Krasil’shchik coupled KdV–mKdV system. By extending Lie symmetry analysis method to a fractional system, two vector fields are derived. The similarity transformation elegantly reduces the fractional system to a set of ordinary differential equations. Furthermore, the explicit power series solutions for the system are derived by employing the power series theory. Lastly, conservation laws for the system are established utilizing Ibragimov’s method.
ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-024-01152-3