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Modeling Water Waves Beyond Perturbations

  • Didier ClamondEmail author
  • Denys Dutykh
Part of the Lecture Notes in Physics book series (LNP, volume 908)

Abstract

In this chapter, we illustrate the advantage of variational principles for modeling water waves from an elementary practical viewpoint. The method is based on a ‘relaxed’ variational principle, i.e., on a Lagrangian involving as many variables as possible, and imposing some suitable subordinate constraints. This approach allows the construction of approximations without necessarily relying on a small parameter. This is illustrated via simple examples, namely the Serre equations in shallow water, a generalization of the Klein–Gordon equation in deep water and how to unify these equations in arbitrary depth. The chapter ends with a discussion and caution on how this approach should be used in practice.

Keywords

Velocity Field Variational Principle Water Wave Lagrangian Density Gordon Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Laboratoire J. A. DieudonnéUniversité de Nice – Sophia AntipolisNice Cedex 2France
  2. 2.Université Savoie Mont Blanc, LAMA, UMR 5127 CNRSLe Bourget-du-Lac CedexFrance

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