Stochastic wave self-modulation in nonequilibrium media

A numerical experiment and qualitative analysis are used to illustrate and investigate the randomness that results from the development of a modulational instability in a nonequilibrium dispersive medium with a spectrally narrow amplification increment. A detailed analysis is performed for a three-mode model describing the modulational decay of two quanta in the same state into a symmetric (+ and -) pair on the assumption that the original quanta are produced because of the nonequilibrium of the medium and that the + and - quanta vanish due to dissipation. An attractor is found in the phase space of the system; the motion of the system at this attractor is aperiodic and describes the complex dynamics. The results indicate that the attractor has Kantor structure and that the motion at it is characterized by a continuous spectrum.