Book Sections Year : 2015

Modeling water waves beyond perturbations

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.
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Dates and versions

hal-01102120 , version 1 (12-01-2015)

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Didier Clamond, Denys Dutykh. Modeling water waves beyond perturbations. Springer. New approaches to nonlinear waves, 908, Springer International Publishing, pp.197-210, 2015, New Approaches to Nonlinear Waves, 978-3-319-20690-5. ⟨10.1007/978-3-319-20690-5_7⟩. ⟨hal-01102120⟩
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