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). pp. 759-773.
Available under License : See the attached licence file.
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.
|Divisions :||Faculty of Engineering and Physical Sciences > Mathematics|
|Identification Number :||https://doi.org/10.1137/040604455|
|Additional Information :||© 2005 Society for Industrial and Applied Mathematics|
|Depositing User :||Mr Adam Field|
|Date Deposited :||16 Mar 2012 14:32|
|Last Modified :||09 Jun 2014 13:27|
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