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.
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Denys Dutykh, Marx Chhay, Didier Clamond. Numerical study of the generalised Klein-Gordon equations. Physica D: Nonlinear Phenomena, Elsevier, 2015, 304-305, pp.23-33. ⟨http://www.sciencedirect.com/science/article/pii/S0167278915000603⟩. ⟨10.1016/j.physd.2015.04.001⟩. ⟨hal-00851030v2⟩

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