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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Veröffentlicht in:	arXiv.org 2015-11
Hauptverfasser:	Marx Chhay, Dutykh, Denys, Clamond, Didier
Format:	Artikel
Sprache:	eng
Schlagworte:	Finite difference method Mathematical models Mathematics - Analysis of PDEs Nonlinear equations Physics - Atmospheric and Oceanic Physics Physics - Exactly Solvable and Integrable Systems Physics - Fluid Dynamics Physics - Geophysics Shallow water Surface waves
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Zusammenfassung:	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