Abstract
The existence of discrete dissipative solitons in a nonlinear lattice is studied. The Ablowitz-Ladik (AL) model with linear damping, nonlinear cubic amplification, quintic damping and complex second difference, representing the discrete analogue of a filter, is investigated. The parameters of the discrete dissipative soliton are calculated using a perturbation theory for the AL model. Analytic predictions are confirmed by numerical simulations of the AL model with non-conservative perturbations. We also discuss modulational instability (MI) in the discrete complex Ginzburg-Landau (DCGL) equation and the existence the exact localized solutions.
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Abdullaev, F. Discrete Dissipative Solitons. In: Akhmediev, N., Ankiewicz, A. (eds) Dissipative Solitons. Lecture Notes in Physics, vol 661. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10928028_13
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DOI: https://doi.org/10.1007/10928028_13
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