Abstract
Motivated from curved waveguides embedded in photonic crystals, 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. The analytical results 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.
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Gaididei, Y., Christiansen, P., Kevrekidis, P., Büttner, H., Bishop, A. (2004). Linear and Nonlinear Bound States in Curved Waveguides. In: Abdullaev, F.K., Konotop, V.V. (eds) Nonlinear Waves: Classical and Quantum Aspects. NATO Science Series II: Mathematics, Physics and Chemistry, vol 153. Springer, Dordrecht. https://doi.org/10.1007/1-4020-2190-9_8
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DOI: https://doi.org/10.1007/1-4020-2190-9_8
Publisher Name: Springer, Dordrecht
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