https://doi.org/10.1140/epjp/s13360-024-05257-1
Regular Article
Lax pair, conservation laws, breather-to-soliton transitions and modulation instability for a coupled extended modified Korteweg-de Vries system in a fluid
State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, 100876, Beijing, China
Received:
11
December
2023
Accepted:
8
May
2024
Published online:
7
June
2024
The modified Korteweg-de Vries-type equations can be used to describe the interfacial waves in a fluid, elastic quasi-plane waves in a lattice, and Alfvén waves in a collisionless plasma. In this paper, we investigate a coupled extended modified Korteweg-de Vries system in a fluid. We construct a Lax pair and obtain some infinitely-many conservation laws under our Lax pair. The first-order breathers and first-order breather-to-soliton transition condition are derived. Under the first-order breather-to-soliton transition condition, we derive the W-shaped solitons, M-shaped solitons, anti-dark solitons and periodic waves. Finally, we discuss the modulation instability for the aforementioned system via the linear stability analysis.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. 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.
