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Gravity-Capillary and Flexural-Gravity Solitary Waves

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Nonlinear Water Waves

Abstract

Solitary gravity-capillary and flexural-gravity waves in two and three dimensions of space are reviewed in this paper. Numerical methods used to compute the solitary waves are described in detail and typical solutions found over the years are presented. Similarities and differences between the solutions for the two physical problems are discussed.

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Acknowledgements

The authors are grateful to the Erwin Schrödinger International Institute for Mathematics and Physics, Vienna, for the support and hospitality during the 2017 Nonlinear Water Waves—an Interdisciplinary Interface workshop. This work was partially supported by EPSRC grants EP/J019305/1 for Emilian I. Părău and EP/J019569/1 for Jean-Marc Vanden-Broeck.

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Authors and Affiliations

  1. School of Mathematics, University of East Anglia, Norwich, UK

    Emilian I. Părău

  2. Department of Mathematics, University College London, London, UK

    Jean-Marc Vanden-Broeck

Authors
  1. Emilian I. Părău
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  2. Jean-Marc Vanden-Broeck
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Correspondence to Emilian I. Părău .

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Editors and Affiliations

  1. School of Mathematical Sciences, University College Cork, Cork, Ireland

    David Henry

  2. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK

    Konstantinos Kalimeris

  3. School of Mathematics, University of East Anglia, Norwich, UK

    Emilian I. Părău

  4. Department of Mathematics, University College London, London, UK

    Jean-Marc Vanden-Broeck

  5. Centre for Mathematical Sciences, Lund University, Lund, Sweden

    Erik Wahlén

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Părău, E.I., Vanden-Broeck, JM. (2019). Gravity-Capillary and Flexural-Gravity Solitary Waves. In: Henry, D., Kalimeris, K., Părău, E., Vanden-Broeck, JM., Wahlén, E. (eds) Nonlinear Water Waves . Tutorials, Schools, and Workshops in the Mathematical Sciences . Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-33536-6_11

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