The fractional nonlinear $${\mathcal{PT}}$$ PT dimer

The fractional nonlinear $${\mathcal{PT}}$$ PT dimer

Abstract We examine a fractional discrete nonlinear Schrodinger dimer, where the usual first-order derivative in the time evolution is replaced by a non integer-order derivative. The dimer is nonlinear (Kerr) and $${\mathcal{{PT}}}$$ PT -symmetric, and for localized initial conditions we examine the...

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Autor principal: Mario I. Molina
Formato: article
Lenguaje:EN
Publicado: Nature Portfolio 2021
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Science
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Acceso en línea:https://doaj.org/article/ac6a7341ff4e496fbdeeafadb916f8a8
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spelling oai:doaj.org-article:ac6a7341ff4e496fbdeeafadb916f8a82021-12-02T14:35:40ZThe fractional nonlinear $${\mathcal{PT}}$$ PT dimer10.1038/s41598-021-89484-x2045-2322https://doaj.org/article/ac6a7341ff4e496fbdeeafadb916f8a82021-05-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-89484-xhttps://doaj.org/toc/2045-2322Abstract We examine a fractional discrete nonlinear Schrodinger dimer, where the usual first-order derivative in the time evolution is replaced by a non integer-order derivative. The dimer is nonlinear (Kerr) and $${\mathcal{{PT}}}$$ PT -symmetric, and for localized initial conditions we examine the exchange dynamics between both sites. By means of the Laplace transformation technique, the linear $${{\mathcal{{PT}}}}$$ PT dimer is solved in closed form in terms of Mittag–Leffler functions, while for the nonlinear regime, we resort to numerical computations using the direct explicit Grunwald algorithm. In general, we see that the main effect of the fractional derivative is to produce a monotonically decreasing time envelope for the amplitude of the oscillatory exchange. In the presence of $${\mathcal{{PT}}}$$ PT symmetry, the oscillations experience some amplification for gain/loss values below some threshold, while beyond threshold, the amplitudes of both sites grow unbounded. The presence of nonlinearity can arrest the unbounded growth and lead to a selftrapped state. The trapped fraction decreases as the nonlinearity is increased past a critical value, in marked contrast with the standard (non-fractional) case.Mario I. MolinaNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-8 (2021)
institution DOAJ
collection DOAJ
language EN
topic Medicine
R
Science
Q
spellingShingle Medicine
R
Science
Q
Mario I. Molina
The fractional nonlinear $${\mathcal{PT}}$$ PT dimer
description Abstract We examine a fractional discrete nonlinear Schrodinger dimer, where the usual first-order derivative in the time evolution is replaced by a non integer-order derivative. The dimer is nonlinear (Kerr) and $${\mathcal{{PT}}}$$ PT -symmetric, and for localized initial conditions we examine the exchange dynamics between both sites. By means of the Laplace transformation technique, the linear $${{\mathcal{{PT}}}}$$ PT dimer is solved in closed form in terms of Mittag–Leffler functions, while for the nonlinear regime, we resort to numerical computations using the direct explicit Grunwald algorithm. In general, we see that the main effect of the fractional derivative is to produce a monotonically decreasing time envelope for the amplitude of the oscillatory exchange. In the presence of $${\mathcal{{PT}}}$$ PT symmetry, the oscillations experience some amplification for gain/loss values below some threshold, while beyond threshold, the amplitudes of both sites grow unbounded. The presence of nonlinearity can arrest the unbounded growth and lead to a selftrapped state. The trapped fraction decreases as the nonlinearity is increased past a critical value, in marked contrast with the standard (non-fractional) case.
format article
author Mario I. Molina
author_facet Mario I. Molina
author_sort Mario I. Molina
title The fractional nonlinear $${\mathcal{PT}}$$ PT dimer
title_short The fractional nonlinear $${\mathcal{PT}}$$ PT dimer
title_full The fractional nonlinear $${\mathcal{PT}}$$ PT dimer
title_fullStr The fractional nonlinear $${\mathcal{PT}}$$ PT dimer
title_full_unstemmed The fractional nonlinear $${\mathcal{PT}}$$ PT dimer
title_sort fractional nonlinear $${\mathcal{pt}}$$ pt dimer
publisher Nature Portfolio
publishDate 2021
url https://doaj.org/article/ac6a7341ff4e496fbdeeafadb916f8a8
work_keys_str_mv AT marioimolina thefractionalnonlinearmathcalptptdimer
AT marioimolina fractionalnonlinearmathcalptptdimer
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