Gravity-Capillary and Flexural-Gravity Solitary Waves

  • Emilian I. PărăuEmail author
  • Jean-Marc Vanden-Broeck
Part of the Tutorials, Schools, and Workshops in the Mathematical Sciences book series (TSWMS)


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.


Solitary waves Flexural-gravity Gravity-capillary 

Mathematics Subject Classification (2000)

Primary 76B25; Secondary 76B45 



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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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of MathematicsUniversity of East AngliaNorwichUK
  2. 2.Department of MathematicsUniversity College LondonLondonUK

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