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.
Domains
Fluid mechanics [physics.class-ph] Fluids mechanics [physics.class-ph] Numerical Analysis [math.NA] Classical Analysis and ODEs [math.CA] Computational Physics [physics.comp-ph] General Physics [physics.gen-ph] Fluid Dynamics [physics.flu-dyn] Atmospheric and Oceanic Physics [physics.ao-ph] Pattern Formation and Solitons [nlin.PS] Exactly Solvable and Integrable Systems [nlin.SI] Analysis of PDEs [math.AP]
Origin : Files produced by the author(s)
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