The fractional discrete nonlinear Schrodinger equation
Author
dc.contributor.author
Molina, Mario I.
Admission date
dc.date.accessioned
2020-05-11T22:23:38Z
Available date
dc.date.available
2020-05-11T22:23:38Z
Publication date
dc.date.issued
2020
Cita de ítem
dc.identifier.citation
Physics Letters A 384 (2020) 126180
es_ES
Identifier
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10.1016/j.physleta.2019.126180
Identifier
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https://repositorio.uchile.cl/handle/2250/174662
Abstract
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We examine a fractional version of the discrete nonlinear Schrodinger (dnls) equation, where the usual discrete laplacian is replaced by a fractional discrete laplacian. This leads to the replacement of the usual nearest-neighbor interaction to a long-range intersite coupling that decreases asymptotically as a power-law. For the linear case, we compute both, the spectrum of plane waves and the mean square displacement of an initially localized excitation in closed form, in terms of regularized hypergeometric functions, as a function of the fractional exponent. In the nonlinear case, we compute numerically the low-lying nonlinear modes of the system and their stability, as a function of the fractional exponent of the discrete laplacian. The selftrapping transition threshold of an initially localized excitation shifts to lower values as the exponent is decreased and, for a fixed exponent and zero nonlinearity, the trapped fraction remains greater than zero.
es_ES
Patrocinador
dc.description.sponsorship
Comision Nacional de Investigacion Cientifica y Tecnologica (CONICYT), CONICYT FONDECYT: 1160177.