| The dynamics of dissipative solitons in systems with rapidly and randomly varying parameters are studied. Two models are considered: the complex Ginzburg-Landau(GL) equation with strong and random modulations of the nonlinearity and dispersion in time. The first model describes the attractive Bose-Einstein condensate with a rapidly varying in time atomic scattering length (via the Feshbach resonance management). The nonconservative terms are related to the atom feeding from the thermal cloud and two- and three-body inelastic processes in atomic collisions. I show the existence of the dissipative solitons in such system using the method of moments and full numerical simulations of the complex GL equation with rapidly varying nonlinearity. The second model describes the dynamics of dissipative solitons in optical fibers with random dispersion management. The linear and nonlinear gains and/or amplification and filters are taken into account. The existence of the dissipative solitons in such media is confirmed analytically and numerically. |
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