Efficient numerical continuation and stability analysis of spatiotemporal quadratic optical solitons

Lloyd, DJB and Champneys, AR (2005) Efficient numerical continuation and stability analysis of spatiotemporal quadratic optical solitons SIAM JOURNAL ON SCIENTIFIC COMPUTING, 27 (3). 759 - 773. ISSN 1064-8275

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Abstract

A numerical method is set out which efficiently computes stationary (z-independent) two- and three-dimensional spatiotemporal solitons in second-harmonic-generating media. The method relies on a Chebyshev decomposition with an infinite mapping, bunching the collocation points near the soliton core. Known results for the type-I interaction are extended and a stability boundary is found by two- parameter continuation as defined by the Vakhitov-Kolokolov criteria. The validity of this criterion is demonstrated in (2+1) dimensions by simulation and direct calculation of the linear spectrum. The method has wider applicability for general soliton-bearing equations in (2+1) and (3+1) dimensions.

Item Type:	Article
Additional Information:	© 2005 Society for Industrial and Applied Mathematics
Divisions:	Faculty of Engineering and Physical Sciences > Mathematics
Depositing User:	Mr Adam Field
Date Deposited:	16 Mar 2012 14:32
Last Modified:	09 Jun 2014 13:27
URI:	http://epubs.surrey.ac.uk/id/eprint/294643

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