%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 }