THE FORMATION OF NONLINEAR WAVE-GUIDES IN THE RESONANT INTERACTION OF3 SURFACE-WAVES

The resonant interaction of three two-dimensional wave packets of capi llary and flexural-gravitational waves on the surface of an infinitely deep ideal liquid is investigated. Universal asymptotic equations are obtained using the Hamiltonian approach. The main types of decaying i nteractions are determined as a function of the group velocities of th e wave packets. New exact waveguide-type solutions of the equations de scribing the interaction between three waves are obtained and investig ated taking dispersion into account. By reducing the dynamical system to a central manifold it is proved that a wide class of solutions of t he waveguide type exists, which depend on five arbitrary constants. It is proved that they are stable with respect to slow changes in the wa veguide boundaries and in the amplitudes of the waves propagating alon g it. (C) 1997 Elsevier Science Ltd. All rights reserved.