Chaotic Solutions of Nonlinear Wave-Wave Interacting Systems in Plasmas.

We study the chaotic behavior and phase locking in wave-wave interacting systems with linear damping or growth terms. For a two or three-wave interaction, the system equations are reducible to a real three-dimensional equation on a certain set, sigma, in the state space. For a three-wave interaction, the phases of the waves are locked on sigma. We consider only systems of positive-energy waves whose reduced equations may have chaotic behavior for almost all initial conditions.