Breakdown of the modulational approximation in a multimode extension of the triplet interaction

• The three wave interaction in a multi-mode environment is studied.
• The analysis is not restricted to slow modulational approximations.
• Abrupt regime transitions arise as a result of the full analysis.

The present work investigates the breakdown of the modulational approximation in a multimode extension of the three wave nonlinear interaction. The modulational approach provides a simplified framework to describe the triplet interaction in regimes where the carrier frequency is much larger than the modulational frequency. The approach is frequently stretched to its limits and beyond, and in the present work we argue that those limits can be in fact quite restrictive. At very small couplings we show that all modes exhibit slow amplitude modulations, but as the coupling increases a transition soon takes place and the modes jump to a new dynamical regime where none can be any longer seen as slowly modulated high-frequency harmonic carriers. Estimates for the critical coupling and relaxation times can be obtained with proper analysis of the most unstable triplet (Iorra et al., 2015).