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

TL;DR

This paper reveals a multi-symplectic structure in the Serre-Green-Naghdi equations, enabling the development of numerical schemes that exactly preserve this structure for modeling nonlinear shallow water waves.

Contribution

It introduces a multi-symplectic formulation of the SGN equations, facilitating structure-preserving numerical methods for shallow water wave simulations.

Findings

Multi-symplectic structure of SGN equations established

Enables structure-preserving finite difference and spectral schemes

Improves numerical stability and accuracy in wave modeling

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.