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:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2016-01, Vol.49 (3), p.3
Main Authors: Chhay, Marx, Dutykh, Denys, Clamond, Didier
Format: Article
Language:English
Subjects:
Analysis of PDEs
Atmospheric and Oceanic Physics
Exactly Solvable and Integrable Systems
Fluid Dynamics
Fluid mechanics
fully nonlinear long waves
Green-Naghdi model
Mathematical analysis
Mathematical models
Mathematical Physics
Mathematics
Mechanics
Modelling
multi-symplectic structure
Nonlinear Sciences
Nonlinearity
Physics
Preserving
Serre equations
Shallow water
Surface waves
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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:1751-8113
1751-8121
DOI:10.1088/1751-8113/49/3/03LT01