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.