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

Christian, J M, McDonald, G S, 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: Colleges and Schools > College of Science & Technology
    Colleges and Schools > College of Science & Technology > School of Computing, Science and Engineering > Materials & Physics Research Centre
    Colleges and Schools > College of Science & Technology > School of Computing, Science and Engineering
    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 13:20
    Last Modified: 06 Jun 2014 07:56
    URI: http://usir.salford.ac.uk/id/eprint/26920

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