Numerical study of the generalised Klein-Gordon equations
arXiv:1308.2521 · 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.
24 pages, 10 figures, 56 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/