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Dissipative solitons in the discrete Ginzburg-Landau equation with saturable nonlinearity
Fatkhulla Kh Abdullaev1, Mario Salerno2
1Physical-Technical Institute, Uzbek Academy of Sciences, 100084 Tashkent, Uzbekistan.
Abstract:
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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