Localised nonlinear optical modes and the corresponding support structures: exact solutions to the nonlinear Schrodinger equation with external potentials

Malomed, B. A. and Stepanyants, Y. A. (2010) Localised nonlinear optical modes and the corresponding support structures: exact solutions to the nonlinear Schrodinger equation with external potentials. In: ICEAA 2010: International Conference on Electromagnetics in Advanced Applications , 20-24 Sep 2010, Sydney, Australia.

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Abstract

Two analytical techniques for the generation of wide classes of exact solutions of the nonlinear Schrödinger equation (NLSE) containing an external potential are proposed. Both methods are illustrated by a variety of localized solutions, including solitary optical vortices, for both the self-focusing and self-defocusing nonlinearities. The stability of solutions was tested by direct numerical simulations of the NLSE; the existence of stable localized modes was confirmed through the simulation.


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Item Type: Conference or Workshop Item (Commonwealth Reporting Category E) (Paper)
Refereed: Yes
Item Status: Live Archive
Additional Information: Published by IEEE (Conferences). Author's version deposited in accordance with the copyright policy of the publisher. © 2010 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purpose or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Depositing User: Assoc Prof Yury Stepanyants
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 16 Dec 2010 13:03
Last Modified: 03 Jul 2013 00:06
Uncontrolled Keywords: electromagnetic waves; nonlinear optical waveguides; nonlinear Schrödinger equation; exact solutions; Korteweg–de Vries equation; soliton; optical vortices; self-focusing medium
Fields of Research (FOR2008): 01 Mathematical Sciences > 0105 Mathematical Physics > 010599 Mathematical Physics not elsewhere classified
02 Physical Sciences > 0205 Optical Physics > 020503 Nonlinear Optics and Spectroscopy
01 Mathematical Sciences > 0102 Applied Mathematics > 010299 Applied Mathematics not elsewhere classified
Socio-Economic Objective (SEO2008): E Expanding Knowledge > 97 Expanding Knowledge > 970102 Expanding Knowledge in the Physical Sciences
E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: doi: 10.1109/ICEAA.2010.5651681
URI: http://eprints.usq.edu.au/id/eprint/9030

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