Localization of nonlinear excitations in curved waveguides

Details Localization of nonlinear excitations in curved waveguides Localization of nonlinear excitations in curved waveguides

2004-09-06

arxiv.org/abs/nlin/0409010v1

Nonlinear Sciences

Pattern Formation and Solitons

14 pages, 4 figures

Scientific paper

10.1088/1367-2630/7/1/052

Motivated by the example of a curved waveguide embedded in a photonic crystal, we examine the effects of geometry in a ``quantum channel'' of parabolic form. We study the linear case and 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 localized excitations are found to persist, as well as to have interesting relaxational dynamics. Analogies of the present problem in contexts related to atomic physics and particularly to Bose-Einstein condensation are discussed.

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