Localization of nonlinear excitations in curved waveguides

Yu. B. Gaididei, Peter Leth Christiansen, P. G. Kevrekidis, H. Büttner, A. R. Bishop

    Research output: Contribution to journalJournal articleResearchpeer-review


    Motivated by the examples of a curved waveguide embedded in a photonic crystal and cold atoms moving in a waveguide created by a spatially inhomogeneous electromagnetic field, we examine the effects of geometry in a 'quantum channel' of parabolic form. Starting with the linear case we derive exact as well as approximate expressions for the eigenvalues and eigenfunctions of the linear problem. We then proceed to the nonlinear setting and its stationary states in a number of limiting cases that allow for analytical treatment. The results of our analysis are used as initial conditions in direct numerical simulations of the nonlinear problem and in this case localized excitations are found to persist. We found also interesting relaxational dynamics. Analogies of the present problem in context related to atomic physics and particularly to Bose–Einstein condensation are discussed.
    Original languageEnglish
    JournalNew Journal of Physics
    Issue number1
    Pages (from-to)52
    Publication statusPublished - 2005


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