https://doi.org/10.1140/epjs/s11734-025-01848-w
Regular Article
On the Lax integrability of a generalized fifth-order KdV model with time-dependent coefficients in fluid dynamics
1
School of Physics, Beihang University, 100191, Beijing, China
2
School of Mathematical Sciences, Beihang University, 100191, Beijing, China
a
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Received:
15
April
2025
Accepted:
4
August
2025
Published online:
14
August
2025
Abstract
This study presents a comprehensive analysis of a generalized fifth-order Korteweg–de Vries model with time-dependent coefficients, under specific Lax integrability conditions derived from the Ablowitz–Kaup–Newell–Segur system. We systematically derive both the 
-Riccati-type and Wahlquist–Estabrook-type Bäcklund transformations, which provide a foundation for generating exact solutions. In addition, the framework allows for the derivation of infinitely many conservation laws, highlighting the model’s rich integrable properties. This work contributes to the understanding of higher order Korteweg–de Vries equations in the shallow water wave theory.
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Tianwei Qiu and Xingjia He contributed equally to this work.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
