Beyond the modulational approximation in the wave triplet interaction

The present work investigates the breakdown of the traditional modulational approximation in the three wave nonlinear interaction, the wave triplet interaction. A common way to describe the interaction of three high-frequency carriers is to assume that amplitudes and phases are slowly modulated. This is the basis of the modulational approach, which is accurate when the three wave coupling is weak. We examine the types of dynamics arising when the coupling rises from very small to large values. At large values we detect an abrupt transition where the limited amplitude excursions of the modulational regime reach much larger regions of the appropriate configuration space. Extensions to similar cases are also investigated.