Linear and nonlinear bound states in curved waveguide

Yuri B. Gaididei; Peter Leth Christiansen; P. G. Kevrekidis; H. Büttner; A. R. Bishop

doi:10.1007/1-4020-2190-9_8

Linear and nonlinear bound states in curved waveguide

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

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

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.

Original language	English
Title of host publication	Proceedings of NATO Advanced Research Workshop on Nonlinear Waves: Classical and quantum aspects
Publisher	Kluwer Academic Publishers
Publication date	2004
Pages	107-120
DOIs	https://doi.org/10.1007/1-4020-2190-9_8
Publication status	Published - 2004

Series	N A T O Science Series. Series II: Mathematics, Physics and Chemistry
Volume	153
ISSN	1568-2609

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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, YB, Christiansen, PL, Kevrekidis, PG, Büttner, H & Bishop, AR 2004, Linear and nonlinear bound states in curved waveguide. in Proceedings of NATO Advanced Research Workshop on Nonlinear Waves: Classical and quantum aspects. Kluwer Academic Publishers, N A T O Science Series. Series II: Mathematics, Physics and Chemistry, vol. 153, pp. 107-120. https://doi.org/10.1007/1-4020-2190-9_8

Linear and nonlinear bound states in curved waveguide. / Gaididei, Yuri B.; Christiansen, Peter Leth; Kevrekidis, P. G. et al.
Proceedings of NATO Advanced Research Workshop on Nonlinear Waves: Classical and quantum aspects. Kluwer Academic Publishers, 2004. p. 107-120 (N A T O Science Series. Series II: Mathematics, Physics and Chemistry, Vol. 153).

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

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Gaididei YB, Christiansen PL, Kevrekidis PG, Büttner H, Bishop AR. Linear and nonlinear bound states in curved waveguide. In Proceedings of NATO Advanced Research Workshop on Nonlinear Waves: Classical and quantum aspects. Kluwer Academic Publishers. 2004. p. 107-120. (N A T O Science Series. Series II: Mathematics, Physics and Chemistry, Vol. 153). doi: 10.1007/1-4020-2190-9_8

Linear and nonlinear bound states in curved waveguide

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