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arXiv · 1308.2521

Numerical study of the generalised Klein-Gordon equations

Denys Dutykh·Marx Chhay·Didier Clamond
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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.

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Denys Dutykh, Marx Chhay, Didier Clamond. 2015-03-16. Numerical study of the generalised Klein-Gordon equations. https://doi.org/10.1016/j.physd.2015.04.001

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