# On the multi-symplectic structure of Boussinesq-type systems. II: Geometric discretization

## TL;DR

This paper develops geometric numerical schemes for Boussinesq-type systems, preserving their multi-symplectic and Hamiltonian structures, to improve the simulation of surface wave propagation.

## Contribution

It introduces geometric discretization strategies that maintain the systems' theoretical properties, advancing numerical methods for wave modeling.

## Key findings

- Preservation of multi-symplectic structure in discretization
- Comparison of spatial and temporal discretization strategies
- Enhanced accuracy in wave simulation

## Abstract

In this paper we consider the numerical approximation of systems of Boussinesq-type to model surface wave propagation. Some theoretical properties of these systems (multi-symplectic and Hamiltonian formulations, well-posedness and existence of solitary-wave solutions) were previously analyzed by the authors in Part I. As a second part of the study, considered here is the construction of geometric schemes for the numerical integration. By using the method of lines, the geometric properties, based on the multi-symplectic and Hamiltonian structures, of different strategies for the spatial and time discretizations are discussed and illustrated.