Numerical study of the generalised Klein-Gordon equations

In this study, we discuss an approximate set of equations describing water wave propagating in deep water. These generalized Klein-Gordon (gKG) equations possess a variational formulation, as well as a canonical Hamiltonian and multi-symplectic structures. Periodic travelling wave solutions are cons...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2015-03
Main Authors: Dutykh, Denys, Marx Chhay, Clamond, Didier
Format: Article
Language:English
Subjects:
Deep water
Euler-Lagrange equation
Stability analysis
Traveling waves
Water waves
Wave packets
Wave propagation
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this study, we discuss an approximate set of equations describing water wave propagating in deep water. These generalized Klein-Gordon (gKG) equations possess a variational formulation, as well as a canonical Hamiltonian and multi-symplectic structures. Periodic travelling wave solutions are constructed numerically to high accuracy and compared to a seventh-order Stokes expansion of the full Euler equations. Then, we propose an efficient pseudo-spectral discretisation, which allows to assess the stability of travelling waves and localised wave packets.
ISSN:2331-8422
DOI:10.48550/arxiv.1308.2521