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

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.

10 pages, 1 figure, 30 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/

Cited by in corpus (3)

• On the multi-symplectic structure of Boussinesq-type systems. I: Derivation and mathematical properties
• Serre-type equations in deep water
• Multi-symplectic structure of fully-nonlinear weakly-dispersive internal gravity waves