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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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⟩. ⟨http://link.springer.com/chapter/10.1007%2F978-3-319-20690-5_7⟩. ⟨hal-01102120⟩

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