Wave envelopes with second-order spatiotemporal dispersion: II. Modulational instabilities and dark Kerr solitons

Christian, J M ORCID: https://orcid.org/0000-0003-2742-0569, McDonald, G S ORCID: https://orcid.org/0000-0002-1304-5182, Hodgkinson, T F and Chamorro-Posada, P 2012, 'Wave envelopes with second-order spatiotemporal dispersion: II. Modulational instabilities and dark Kerr solitons' , Physical Review A (PRA), 86 (2) , 023839.

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Abstract

A simple scalar model for describing spatiotemporal dispersion of pulses, beyond the classic “slowly-varying envelopes + Galilean boost” approach, is studied. The governing equation has a cubic nonlinearity and we focus here mainly on contexts with normal group-velocity dispersion. A complete analysis of continuous waves is reported, including their dispersion relations and modulational instability characteristics. We also present a detailed derivation of exact analytical dark solitons, obtained by combining direct-integration methods with geometrical transformations. Classic results from conventional pulse theory are recovered as-ymptotically from the spatiotemporal formulation. Numerical simulations test new theoretical predictions for modulational instability, and examine the robustness of spatiotemporal dark solitons against perturbations to their local pulse shape.

Item Type:	Article
Themes:	Subjects outside of the University Themes
Schools:	Schools > School of Computing, Science and Engineering Schools > School of Computing, Science and Engineering > Salford Innovation Research Centre
Journal or Publication Title:	Physical Review A (PRA)
Publisher:	American Physical Society
Refereed:	Yes
ISSN:	1050-2947
Depositing User:	JM Christian
Date Deposited:	08 Oct 2012 12:20
Last Modified:	15 Feb 2022 16:24
URI:	https://usir.salford.ac.uk/id/eprint/26920

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