A HAMILTONIAN APPROACH TO FAIRLY LOW AND FAIRLY LONG GRAVITY-WAVES

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.