Efficient numerical continuation and stability analysis of spatiotemporal quadratic optical solitons

DJ Lloyd; AR Champneys

Efficient numerical continuation and stability analysis of spatiotemporal quadratic optical solitons

Research output: Working paper

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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 criteria 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.

Original language	English
Publication status	Unpublished - 2004

Bibliographical note

Sponsorship: The authors would like to thank John P. Boyd, Boris A. Malomed and Dimitru Mihalache for their useful remarks. The authors would also like to thank Richard R. Kerswell for initially suggesting the numerical discretisation.

Research Groups and Themes

Engineering Mathematics Research Group

Keywords

optical soliton
second-harmonic-generation
type-I interaction
continuation

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2004r12Submitted manuscript, 2.16 MB

http://hdl.handle.net/1983/71

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1 Article (Academic Journal)

Efficient numerical continuation and stability analysis of spatiotemporal quadratic optical solitons
Lloyd, D. & Champneys, A., 2005, In: SIAM Journal on Scientific Computing. 27(3), p. 759 - 773 15 p.
Research output: Contribution to journal › Article (Academic Journal) › peer-review

Cite this

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title = "Efficient numerical continuation and stability analysis of spatiotemporal quadratic optical solitons",

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 criteria 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.",

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Y1 - 2004

N2 - 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 criteria 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.

AB - 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 criteria 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.

KW - optical soliton

KW - second-harmonic-generation

KW - type-I interaction

KW - continuation

M3 - Working paper

BT - Efficient numerical continuation and stability analysis of spatiotemporal quadratic optical solitons

ER -

Efficient numerical continuation and stability analysis of spatiotemporal quadratic optical solitons

Abstract

Bibliographical note

Research Groups and Themes

Keywords

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Research output

Efficient numerical continuation and stability analysis of spatiotemporal quadratic optical solitons

Cite this