Multi-symplectic structure of fully-nonlinear weakly-dispersive internal gravity waves

Abstract : In this short communication we present the multi-symplectic structure for the two-layer Serre-Green-Naghdi equations describing the evolution of large amplitude internal gravity long waves. We consider only a two-layer stratification with rigid bottom and lid for simplicity, generalisations to several layers being straightforward. This multi-symplectic formulation allows the application of various multi-symplectic integrators (such as Euler or Preissman box schemes) that preserve exactly the multi-symplecticity at the discrete level.
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Didier Clamond, Denys Dutykh. Multi-symplectic structure of fully-nonlinear weakly-dispersive internal gravity waves. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2016, 49, pp.31LT01. ⟨http://iopscience.iop.org/article/10.1088/1751-8113/49/31/31LT01⟩. ⟨10.1088/1751-8113/49/31/31LT01⟩. ⟨hal-01296552v2⟩

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