Physical-Technical Institute, Uzbek Academy of Sciences, 100084 Tashkent, Uzbekistan.
Dipartimento di Fisica E.R. Caianiello and INFN, Gruppo Collegato di Salerno, Universita di Salerno, Via Giovanni Paolo II, 84084 Fisciano, Salerno, Italy.
Phys Rev E. 2018 May;97(5-1):052208. doi: 10.1103/PhysRevE.97.052208.
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.
研究了具有饱和非线性的离散 Ginzburg-Landau 方程中非线性平面波的调制不稳定性和周期和局域耗散孤子和波的存在。导出了具有零和有限背景的周期解的显式解析表达式，并通过直接数值模拟研究了它们的稳定性。我们发现，虽然零背景下的离散周期波和孤子在时间演化下是稳定的，但它们在有限背景下可能变得调制不稳定。还简要讨论了线性斜坡势对稳定局域耗散孤子的影响。
