NONLINEAR COHERENT MULTIWAVE MODES - UNIVERSAL INTEGRALS OF MOTION AND EFFECTIVE HAMILTONIAN

It is shown that a resonant nonlinear interaction of waves may result in a variety of collective multiwave modes of coherent resonantly coup led waves. The equations of motion for the modes have a universal set of integrals (''collision constants'') reflecting a ''particle balance '' (in quantum-mechanical terms) in wave collisions. The existence of these integrals ensures that the collective modes are completely integ rable. Any multiwave mode can be described by an effective single degr ee of freedom conservative Hamiltonian, similar to the one known for t hree-wave coherent modes (triads).