On the multi-symplectic structure of the Serre-Green-Naghdi equations

In this short note, we present a multi-symplectic structure of the Serre-Green-Naghdi (SGN) equations modelling nonlinear long surface waves in shallow water. This multi-symplectic structure allow the use of efficient finite difference or pseudo-spectral numerical schemes preserving exactly the mult...

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Bibliographic Details
Published in:arXiv.org 2015-11
Main Authors: Marx Chhay, Dutykh, Denys, Clamond, Didier
Format: Article
Language:English
Subjects:
Finite difference method
Mathematical models
Nonlinear equations
Shallow water
Surface waves
Online Access:Get full text
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Summary:In this short note, we present a multi-symplectic structure of the Serre-Green-Naghdi (SGN) equations modelling nonlinear long surface waves in shallow water. This multi-symplectic structure allow the use of efficient finite difference or pseudo-spectral numerical schemes preserving exactly the multi-symplectic form at the discrete level.
ISSN:2331-8422
DOI:10.48550/arxiv.1511.00612