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Optics Letters

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  • Vol. 30, Iss. 16 — Aug. 15, 2005
  • pp: 2140–2142

Spectral renormalization method for computing self-localized solutions to nonlinear systems

Mark J. Ablowitz and Ziad H. Musslimani  »View Author Affiliations


Optics Letters, Vol. 30, Issue 16, pp. 2140-2142 (2005)
http://dx.doi.org/10.1364/OL.30.002140


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Abstract

A new numerical scheme for computing self-localized states - or solitons - of nonlinear waveguides is proposed. The idea behind the method is to transform the underlying equation governing the soliton, such as a nonlinear Schrödinger-type equation, into Fourier space and determine a nonlinear nonlocal integral equation coupled to an algebraic equation. The coupling prevents the numerical scheme from diverging. The nonlinear guided mode is then determined from a convergent fixed point iteration scheme. This spectral renormalization method can find wide applications in nonlinear optics and related fields such as Bose-Einstein condensation and fluid mechanics.

© 2005 Optical Society of America

OCIS Codes
(000.0000) General : General
(000.2690) General : General physics

Citation
Mark J. Ablowitz and Ziad H. Musslimani, "Spectral renormalization method for computing self-localized solutions to nonlinear systems," Opt. Lett. 30, 2140-2142 (2005)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-30-16-2140


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