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      Solitary flexural–gravity waves in three dimensions

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          Abstract

          The focus of this work is on three-dimensional nonlinear flexural–gravity waves, propagating at the interface between a fluid and an ice sheet. The ice sheet is modelled using the special Cosserat theory of hyperelastic shells satisfying Kirchhoff's hypothesis, presented in (Plotnikov & Toland. 2011 Phil. Trans. R. Soc. A 369, 2942–2956 ( doi:10.1098/rsta.2011.0104)). The fluid is assumed inviscid and incompressible, and the flow irrotational. A numerical method based on boundary integral equation techniques is used to compute solitary waves and forced waves to Euler's equations.

          This article is part of the theme issue ‘Modelling of sea-ice phenomena’.

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          Most cited references45

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          Gravity-capillary solitary waves in water of infinite depth and related free-surface flows

          Frédéric Dias, Jean-Marc Vanden-Broeck (1992)
          Article 0 comments Cited 26 times – based on 0 reviews     Review now
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            Wave Motion in Hydrodynamics

            A. Greenhill (1886)
            Article 0 comments Cited 26 times – based on 0 reviews     Review now
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              On a new non-local formulation of water waves

              M. Ablowitz, A. Fokas, Z Musslimani (2006)
              Article 0 comments Cited 20 times – based on 0 reviews     Review now
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                Author and article information

                Journal
                Journal ID (nlm-ta): Philos Trans A Math Phys Eng Sci
                Journal ID (iso-abbrev): Philos Trans A Math Phys Eng Sci
                Journal ID (publisher-id): RSTA
                Journal ID (hwp): roypta
                Title: Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
                Publisher: The Royal Society Publishing
                ISSN (Print): 1364-503X
                ISSN (Electronic): 1471-2962
                Publication date (Print): 28 September 2018
                Publication date (Electronic): 20 August 2018
                Publication date PMC-release: 20 August 2018
                Volume: 376
                Issue: 2129 , Theme issue ‘Modelling of sea-ice phenomena’ compiled and edited by Frank Smith, Alexander Korobkin, Emilian Parau, Daniel Feltham and Vernon Squire
                Electronic Location Identifier: 20170345
                Affiliations
                [1 ]Department of Physics and Astronomy, University of Western Ontario , London, Ontario, Canada
                [2 ]School of Mathematics, University of East Anglia , Norwich, UK
                [3 ]Department of Mathematics, University College London , Gower Street, London, UK
                [4 ]Department of Mathematical Sciences, University of Bath , Claverton Down, Bath, UK
                Author notes

                One contribution of 15 to a theme issue ‘ Modelling of sea-ice phenomena’.

                Author information
                http://orcid.org/0000-0001-5134-2068
                Article
                Publisher ID: rsta20170345
                DOI: 10.1098/rsta.2017.0345
                PMC ID: 6107609
                PubMed ID: 30126916
                SO-VID: 89f33ab1-a061-4bac-8cd6-c2169165250b
                Copyright © © 2018 The Authors.
                License:

                Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.

                History
                Date accepted : 19 June 2018
                Funding
                Funded by: E.I.P.;
                Award ID: EP/J019305/1
                Funded by: P.M.;
                Award ID: EP/J019321/1
                Funded by: J.-M.V.-B and O.T;
                Award ID: EP/J019569/1
                Funded by: EPSRC;
                Award ID: EP/K032208/1
                Categories
                Subject: 1008
                Subject: 6
                Subject: 1009
                Subject: 73
                Subject: Articles
                Subject: Research Article
                Custom metadata
                cover-date September 28, 2018

                Keywords: solitary waves,flexural–gravity waves,boundary integral method
                Data availability:
                Keywords: solitary waves, flexural–gravity waves, boundary integral method

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