Traditional wave kinetics describes slow evolution of wave spectrum of the system with many degree of freedoms to statistical equilibrium via numerous weakly nonlinear interactions . In classical wave kinetics, initial wave spectrum evolves gradually to a statistically stationary wave spectrum when energy pumping/dumping is homogeneous over the evolution time. The evolution is governed by wave kinetic equation. However, many practically important optical systems, like lasers, are dissipative (active) in their nature. Moreover, in lasers the energy pumping/dumping act in a periodic way resulting in cycling dynamics and double-scale evolution of the wave (i.e. optical) spectrum. When the energy pumping/dumping changes within the cycle, the wave spectrum is locally non-stationary exhibiting strong changes within each cycle. At the same time, the spectrum evolves in a gradual incremental way from cycle to cycle similar to classical wave kinetics. If overall pumping within the cycle is equal to energy dumping, the system approaches the global stationary solution. Traditional wave kinetics cannot be applied for such systems.
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