Abstract
The propagation of nonlinear dispersive gravity waves in an inviscid irrotational fluid can be described by a Hamiltonian system. The canonical equations contain a boundary integral which is computationally expensive. However, for fairly low and fairly long waves an approximation can be made that gives rise to the solution of computationally more attractive Helmholtz-type equations. In an earlier attempt by Broer et al. [4, 6] canonical equations were derived that are stable for all wavenumbers. However, two Helmholtz-type equations need to be solved per right-hand side evaluation. In this paper, canonical equations are presented with the same qualities, but now only once per right-hand side evaluation a Helmholz-type equation needs to be solved, which is optimal.
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van der Veen, W.A., Wubs, F.W. A Hamiltonian approach to fairly low and fairly long gravity waves. J Eng Math 29, 329–345 (1995). https://doi.org/10.1007/BF00042760
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DOI: https://doi.org/10.1007/BF00042760