ON WAVE INTERACTIONS .1. EXPLOSIVE RESONANT TRIADS

This paper considers the phenomenon of explosive resonant triads in we akly nonlinear, dispersive wave systems. These nearly linear waves wit h slowly varying amplitudes become unbounded in finite time. It is sho wn that such interactions are much stronger than previously thought. T hese waves can be thought of as a nonlinear instability in the sense t hat a weakly nonlinear perturbation to some system grows to such a mag nitude that the behavior of the system is governed by strongly nonline ar effects. This may occur for systems that are linearly or neutrally stable. This resolution is contrasted with previous resolutions of the problem, which assumed such perturbations remained large amplitude, n early linear waves. Analytical and numerical evidence is presented to support these claims.