Dissipative finite degrees of freedom dynamical system and description of optical systems with saturable amplification, saturable losses, and filtering

Description of optical system with saturable amplification, saturable losses and filtering9-10 (see also11-12) is studied. The aim of this work is to derive the system of ode's, that extends the earlier one1-2, including additionally the temporal dependences of the saturated gain and losses. First, this extended system is applied to the case of fast changes in the amplification and losses7-8. Regarding the dissipative solitons, earlier results7-8 have been confirmed. In addition, nonlinear fixed points have been also studied and as result fronts were identified. Next, the extended system is applied to the case of temporal dependent amplification and losses9-10. Linear and nonlinear fixed points of this system have been calculated and their stability identified. Typical solutions discussed earlier9 have been found. Fronts have been also revealed. Phase space interpretation of obtained coherent structures is given.