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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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.
|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 (SIRC)
|Journal or Publication Title:||Physical Review A (PRA)|
|Publisher:||American Physical Society|
|Depositing User:||JM Christian|
|Date Deposited:||08 Oct 2012 12:20|
|Last Modified:||30 Nov 2015 23:55|
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