Wa. Vanderveen et Fw. Wubs, A HAMILTONIAN APPROACH TO FAIRLY LOW AND FAIRLY LONG GRAVITY-WAVES, Journal of engineering mathematics, 29(4), 1995, pp. 329-345
The propagation of nonlinear dispersive gravity waves in an inviscid i
rrotational fluid can be described by a Hamiltonian system. The canoni
cal equations contain a boundary integral which is computationally exp
ensive. However, for fairly low and fairly long waves an approximation
can be made that gives rise to the solution of computationally more a
ttractive Helmholtz-type equations. In an earlier attempt by Broer et
al. [4, 6] canonical equations were derived that are stable for all wa
venumbers. However, two Helmholtz-type equations need to be solved per
right-hand side evaluation. In this paper, canonical equations are pr
esented with the same qualities, but now only once per right-hand side
evaluation a Helmholz-type equation needs to be solved, which is opti
mal.