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.
|Publication status||Unpublished - 2004|
Bibliographical noteSponsorship: 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.
- optical soliton
- type-I interaction