2016
DOI: 10.1007/s11082-016-0658-z
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Anderson localization in the quintic nonlinear Schrödinger equation

Abstract: In the present paper we consider the quintic defocusing nonlinear Schrödinger equation in presence of a disordered random potential and we analyze the effects of the quintic nonlinearity on the Anderson localization of the solution. The main result shows that Anderson localization requires a cutoff on the value of the parameter which controls the quintic nonlinearity, with the cutoff depending on the amplitude of the random potential.PACS numbers: 42.25.Dd, 42.65.Tg

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Cited by 8 publications
(1 citation statement)
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“…The Anderson localization has been experimentally demonstrated in many scenarios such as Bose-Einstein condensate (BEC) of atoms [2,3], in 2D [4] and 1D [5] disordered photonic lattices. From the theoretical viewpoint, the Anderson localization has been studied in synthetic photonic lattice with random coupling [6], in biological nanostructures of native silk [7], on the surface plasmon polariton [8], and in Bose-Einstein condensate with a weakly positive nonlinearity under the influence of chaotic potentials [9,10].…”
Section: Introductionmentioning
confidence: 99%
“…The Anderson localization has been experimentally demonstrated in many scenarios such as Bose-Einstein condensate (BEC) of atoms [2,3], in 2D [4] and 1D [5] disordered photonic lattices. From the theoretical viewpoint, the Anderson localization has been studied in synthetic photonic lattice with random coupling [6], in biological nanostructures of native silk [7], on the surface plasmon polariton [8], and in Bose-Einstein condensate with a weakly positive nonlinearity under the influence of chaotic potentials [9,10].…”
Section: Introductionmentioning
confidence: 99%