https://doi.org/10.1140/epjs/s11734-025-01964-7
Regular Article
Emergence of the dark envelope nonlinear surface waves in shallow water
1
College of Physics and Electronic Engineering, Northwest Normal University, 730070, Lanzhou, People’s Republic of China
2
Department of Physics and Hydropower Engineering, Gansu Normal University for Nationalities, 747000, Hezuo, People’s Republic of China
a
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Received:
20
July
2025
Accepted:
15
September
2025
Published online:
22
September
2025
Abstract
This paper explores the nonlinear dynamics of shallow water waves and establishes analytical conditions for the formation of dark envelope solitons. Using perturbation theory, we derive a nonlinear Schrödinger equation with newly formulated dispersion and nonlinearity coefficients, enabling a precise description of shallow-water wave evolution. Explicit dark soliton solutions are obtained, together with a formation criterion linking wave amplitude, water depth, and soliton structure. These findings reveal fundamental mechanisms governing soliton behavior and offer a theoretical basis for controlling wave propagation. The results not only enrich the theoretical framework of shallow-water wave dynamics but also provide practical guidance for wave modeling, benefiting oceanography, coastal engineering, and wave energy applications.
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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.
