https://doi.org/10.1140/epjs/s11734-025-01850-2
Regular Article
Hamiltonian structures, conservation laws, and rogue wave solutions for the higher-order semi-discrete complex modified Korteweg–de Vries equation
1
School of Applied Science, Beijing Information Science and Technology University, 100192, Beijing, China
2
School of Mathematics and Statistics, Henan University, 475004, Kaifeng, China
Received:
20
May
2025
Accepted:
8
August
2025
Published online:
30
August
2025
We derive the Hamiltonian structures and construct an infinite hierarchy of conservation laws for the semi-discrete modified Korteweg–de Vries equation in this paper. Subsequently, leveraging the generalized Darboux transformation, we systematically develop rogue wave solutions for a higher-order semi-discrete modified Korteweg–de Vries equation. To comprehensively elucidate the associated dynamic behavior, we explicitly present the first three-order rogue wave solutions, accompanied by their corresponding graphical visualizations. Additionally, through detailed numerical simulations, we thoroughly analyze the wave propagation characteristics and assess the stability properties of these solutions, thereby providing a comprehensive understanding of the underlying physical phenomena.
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© 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.
