2016
On the multi-symplectic structure of the Serre—Green—Naghdi equations
JJ. Phys. A: Math. Theor.
M. Chhay, D. Dutykh and D. Clamond
J. Phys. A: Math. Theor. 49(03LT01): 03LT01 (2016)
Open Access
Abstract
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.
Keywords
shallow water wavesHamiltonian mechanicsvariational principlesGreen-Naghdi modelnonlinear long surface wavesSerre-Green-Naghdi equationsmulti-symplectic numerical schemesfinite difference methodsfully nonlinear long wavespseudo-spectral methodsmulti-symplectic structureSerre equations
Bibliographic record
BibTeX Citation
@article{Chhay2016multisymplecticstructure,
author = {Chhay, M. and Dutykh, D. and Clamond, D.},
title = {On the multi-symplectic structure of the Serre—Green—Naghdi equations},
journal = {J. Phys. A: Math. Theor.},
year = {2016},
volume = {49},
number = {03LT01},
pages = {03LT01},
doi = {10.1088/1751-8113/49/3/03LT01},
abstract = {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.},
keywords = {shallow water waves, Hamiltonian mechanics, variational principles, Green-Naghdi model, nonlinear long surface waves, Serre-Green-Naghdi equations, multi-symplectic numerical schemes, finite difference methods, fully nonlinear long waves, pseudo-spectral methods, multi-symplectic structure, Serre equations}
}