Abstract Fractional calculus is entering the field of nonlinear optics to describe unconventional regimes, as disorder biological media and soft-matter. Here we investigate spatiotemporal modulational instability (MI) in a fractional nonlinear Schrödinger equation. We derive the \MI\ gain spectrum in terms of the Lévy indexes and a varying number of spatial dimensions. We show theoretically and numerically that the Lévy indexes affect fastest growth frequencies and \MI\ bandwidth and gain. Our results unveil a very rich scenario that may occur in the propagation of ultrashort pulses in random media and metamaterials, and may sustain novel kinds of propagation invariant optical bullets.
%0 Journal Article
%1 Zhang2017
%A Zhang, Lifu
%A He, Zenghui
%A Conti, Claudio
%A Wang, Zhiteng
%A Hu, Yonghua
%A Lei, Dajun
%A Li, Ying
%A Fan, Dianyuan
%D 2017
%J Communications in Nonlinear Science and Numerical Simulation
%K myown
%P -
%R http://dx.doi.org/10.1016/j.cnsns.2017.01.019
%T Modulational instability in fractional nonlinear Schrödinger equation
%U http://www.sciencedirect.com/science/article/pii/S1007570417300266
%X Abstract Fractional calculus is entering the field of nonlinear optics to describe unconventional regimes, as disorder biological media and soft-matter. Here we investigate spatiotemporal modulational instability (MI) in a fractional nonlinear Schrödinger equation. We derive the \MI\ gain spectrum in terms of the Lévy indexes and a varying number of spatial dimensions. We show theoretically and numerically that the Lévy indexes affect fastest growth frequencies and \MI\ bandwidth and gain. Our results unveil a very rich scenario that may occur in the propagation of ultrashort pulses in random media and metamaterials, and may sustain novel kinds of propagation invariant optical bullets.
@article{Zhang2017,
abstract = {Abstract Fractional calculus is entering the field of nonlinear optics to describe unconventional regimes, as disorder biological media and soft-matter. Here we investigate spatiotemporal modulational instability (MI) in a fractional nonlinear Schrödinger equation. We derive the \{MI\} gain spectrum in terms of the Lévy indexes and a varying number of spatial dimensions. We show theoretically and numerically that the Lévy indexes affect fastest growth frequencies and \{MI\} bandwidth and gain. Our results unveil a very rich scenario that may occur in the propagation of ultrashort pulses in random media and metamaterials, and may sustain novel kinds of propagation invariant optical bullets. },
added-at = {2017-01-26T09:42:23.000+0100},
author = {Zhang, Lifu and He, Zenghui and Conti, Claudio and Wang, Zhiteng and Hu, Yonghua and Lei, Dajun and Li, Ying and Fan, Dianyuan},
biburl = {https://www.bibsonomy.org/bibtex/2e182760e1aac8be988e7a68f8a664f18/nonlinearxwaves},
doi = {http://dx.doi.org/10.1016/j.cnsns.2017.01.019},
interhash = {d9a531496a2ce31b6bcc0c947ad3005a},
intrahash = {e182760e1aac8be988e7a68f8a664f18},
issn = {1007-5704},
journal = {Communications in Nonlinear Science and Numerical Simulation },
keywords = {myown},
pages = { - },
timestamp = {2017-01-26T09:50:56.000+0100},
title = {Modulational instability in fractional nonlinear Schrödinger equation },
url = {http://www.sciencedirect.com/science/article/pii/S1007570417300266},
year = 2017
}