Bifurcations and stability of gap solitons in periodic potentials

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dc.creatorPelinovsky, Dmitry E.
dc.creatorSukhorukov, Andrey A.
dc.creatorKivshar, Yuri S.
dc.date2004-05-10
dc.date2004-05-15
dc.date.accessioned2026-07-07T05:35:32Z
dc.date.available2026-07-07T05:35:32Z
dc.descriptionWe analyze the existence, stability, and internal modes of gap solitons in nonlinear periodic systems described by the nonlinear Schrodinger equation with a sinusoidal potential, such as photonic crystals, waveguide arrays, optically-induced photonic lattices, and Bose-Einstein condensates loaded onto an optical lattice. We study bifurcations of gap solitons from the band edges of the Floquet-Bloch spectrum, and show that gap solitons can appear near all lower or upper band edges of the spectrum, for focusing or defocusing nonlinearity, respectively. We show that, in general, two types of gap solitons can bifurcate from each band edge, and one of those two is always unstable. A gap soliton corresponding to a given band edge is shown to possess a number of internal modes that bifurcate from all band edges of the same polarity. We demonstrate that stability of gap solitons is determined by location of the internal modes with respect to the spectral bands of the inverted spectrum and, when they overlap, complex eigenvalues give rise to oscillatory instabilities of gap solitons.
dc.description18 pages, 11 figures; updated bibliography
dc.identifierhttps://arxiv.org/abs/nlin/0405019
dc.identifierhttp://arxiv.org/abs/nlin/0405019
dc.identifierPhys. Rev. E 70, 036618(1-17) (2004).
dc.identifierdoi:10.1103/PhysRevE.70.036618
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/80727
dc.subjectPattern Formation and Solitons
dc.subjectOther Condensed Matter
dc.subjectOptics
dc.titleBifurcations and stability of gap solitons in periodic potentials
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