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Steady dark solitary flexural gravity waves

Milewski, PA; Vanden-Broeck, J-M; Wang, Z; (2013) Steady dark solitary flexural gravity waves. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences , 469 (2150) , Article 20120485. 10.1098/rspa.2012.0485. Green open access

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Abstract

The nonlinear Schrödinger (NLS) equation describes the modulational limit of many surface water wave problems. Dark solitary waves of the NLS equation asymptote to a constant in the far field and have a localized decrease to zero amplitude at the origin, corresponding to water wave solutions that asymptote to a uniform periodic Stokes wave in the far field and decreasing oscillations near the origin. It is natural to ask whether these dark solitary waves can be found in the irrotational Euler equations. In this paper, we find such solutions in the context of flexural-gravity waves, which are often used as a model for waves in ice-covered water. This is a situation in which the NLS equation predicts steadily travelling dark solitons. The solution branches of dark solitons are continued, and one branch leads to fully localized solutions at large amplitudes.

Type: Article
Title: Steady dark solitary flexural gravity waves
Open access status: An open access version is available from UCL Discovery
DOI: 10.1098/rspa.2012.0485
Publisher version: http://dx.doi.org/10.1098/rspa.2012.0485
Language: English
Additional information: Copyright © 2012 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0/), which permits unrestricted use, provided the original author and source are credited.
Keywords: dark solitary waves, water waves, flexural gravity waves
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/1385644
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