Numerical study of the generalised Klein—Gordon equations

Abstract

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.

Keywords

Bibliographic record

BibTeX Citation

@article{Dutykh2015numericalstudy,
  author = {Dutykh, D. and Clamond, D. and Chhay, M.},
  title = {Numerical study of the generalised Klein—Gordon equations},
  journal = {Phys. D},
  year = {2015},
  volume = {304--305},
  pages = {23--33},
  doi = {10.1016/j.physd.2015.04.001},
  abstract = {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.},
  keywords = {stability, spectral methods, travelling waves, periodic waves, deep water approximation}
}