کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1895277 | 1533989 | 2016 | 12 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Modulational instability and localized breather modes in the discrete nonlinear Schrödinger equation with helicoidal hopping Modulational instability and localized breather modes in the discrete nonlinear Schrödinger equation with helicoidal hopping](/preview/png/1895277.png)
We study a one-dimensional discrete nonlinear Schrödinger model with hopping to the first and a selected NNth neighbor, motivated by a helicoidal arrangement of lattice sites. We provide a detailed analysis of the modulational instability properties of this equation, identifying distinctive multi-stage instability cascades due to the helicoidal hopping term. Bistability is a characteristic feature of the intrinsically localized breather modes, and it is shown that information on the stability properties of weakly localized solutions can be inferred from the plane-wave modulational instability results. Based on this argument, we derive analytical estimates of the critical parameters at which the fundamental on-site breather branch of solutions turns unstable. In the limit of large NN, these estimates predict the emergence of an effective threshold behavior, which can be viewed as the result of a dimensional crossover to a two-dimensional square lattice.
Journal: Physica D: Nonlinear Phenomena - Volumes 328–329, 1 August 2016, Pages 9–20