Three-wave interaction in dissipative systems: a new way towards secondary instabilities

Abstract

We have identified a new mechanism of wave destabilization in nonlinear dissipative systems. This mechanism, which differs from the usual scheme of two complex Ginzburg–Landau equations, is associated with a three-wave interaction (TWI) process, in close analogy with nonlinear optics and plasma physics. We develop a paradigm from which we derive the wave number and threshold of the secondary instability. Numerically, we obtain a good agreement with the theoretical predictions. Moreover, we numerically investigate a model which describes a real experiment and exhibits a regime of parameter where this mechanism is involved.