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

Christian, J M; McDonald, G S; Hodgkinson, T F; Chamorro-Posada, P

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.

Citation

II. Modulational instabilities and dark Kerr solitons. Physical Review A, 86(2), 023839. https://doi.org/10.1103/PhysRevA.86.023839

• Journal Article Type: Article
• Publication Date: Aug 1, 2012
• Deposit Date: Oct 8, 2012
• Publicly Available Date: Oct 8, 2012
• Journal: Physical Review A (PRA)
• Print ISSN: 1050-2947
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 86
• Issue: 2
• Pages: 023839
• DOI: https://doi.org/10.1103/PhysRevA.86.023839
• Publisher URL: http://dx.doi.org/10.1103/PhysRevA.86.023839