Dissipative solitons in the discrete Ginzburg-Landau equation with saturable nonlinearity
F. Kh. AbdullaevPhysical-Technical Institute, Uzbek Academy of Sciences, 100084 Tashkent, UzbekistanMario SalernoDipartimento di Fisica E.R. Caianiello and INFN, Gruppo Collegato di Salerno, Universita di Salerno, Via Giovanni Paolo II, 84084 Fisciano, Salerno, Italy
ABI
Аннотация
The modulational instability of nonlinear plane waves and the existence of periodic and localized dissipative solitons and waves of the discrete Ginzburg-Landau equation with saturable nonlinearity are investigated. Explicit analytic expressions for periodic solutions with a zero and a finite background are derived and their stability properties investigated by means of direct numerical simulations. We find that while discrete periodic waves and solitons on a zero background are stable under time evolution, they may become modulationally unstable on finite backgrounds. The effects of a linear ramp potential on stable localized dissipative solitons are also briefly discussed.
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