Reactive and resistive nonlinear instabilities

Abstract

It is argued that familiar nonlinear instabilities, such as three-wave decay instabilities and scattering off quasi-modes, have reactive and resistive versions. In appropriate limits these versions correspond to fixed-phase parametric instabilities and to random phase growth in weak turbulence theory, respectively. Using a simplified model it is shown that the reactive version passes over into the resistive version when the band-width of the pump is comparable with the growth rate.