Nonintegrable three mode interaction in the Zakharov equations

Abstract

In this paper we investigate the behavior of an interacting wave triplet in the context of the Zakharov equations. As the amplitude of the carrier modes grows, the nonlinear modulational frequency with which they exchange energy becomes comparable to their linear high frequencies - in this situation adiabatic approximations can no longer be used. In fact, we find that while for small amplitudes the triplet is approximately integrable and yields almost periodic solutions, for larger amplitudes it develops fully nonintegrable features characteristic of strong chaotic regimes. An appropriate Hamiltonian formalism is developed to describe the dynamics. © 1997 Elsevier Science B.V. All rights reserved.