From modulational instability to self-trapping in nonlinear chains with power-law hopping amplitudes

W.S. Dias, J.F.A. Sousa and M.L. Lyra

Physica A: Statistical Mechanics and its Applications, 2019, vol. 532, issue C

Abstract: The modulational instability problem in tight-binding nonlinear chains with long-ranged hopping amplitudes decaying as 1∕rα is investigated. Exploring that the spectral dimension of the corresponding linear chain deff=2∕(α−1) for α≥3, we demonstrate that the nonlinear strength χMI above which a uniform solution becomes unstable scales with the chain size N as χMI∝N2−α for α≤3 while χMI∝1∕N for α≥3. We also present numerical data unveiling that the intermediate regimes of breathing and chaotic-like solutions appearing during the crossover from the stable uniform solution to self-trapping are fully suppressed when the hopping amplitudes decay slower than 1∕r2.

Keywords: Modulational instability; Self-trapping; Breathing modes; Chaotic dynamics; Long-range couplings (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:532:y:2019:i:c:s0378437119311239

DOI: 10.1016/j.physa.2019.121909

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