Wave envelopes with second-order spatiotemporal dispersion :
I. Bright Kerr solitons and cnoidal waves

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

Abstract

We propose a simple scalar model for describing pulse phenomena beyond the conventional slowly-varying envelope approximation. The generic governing equation has a cubic nonlinearity and we focus here mainly on contexts involving anomalous group-velocity dispersion. Pulse propagation turns out to be a problem firmly rooted in frames-of-reference considerations. The transformation properties of the new model and its space-time structure are explored in detail. Two distinct representations of exact analytical solitons and their associated conservation laws (in both integral and algebraic forms) are presented, and a range of new predictions is made. We also report cnoidal waves of the governing nonlinear equation. Crucially, conventional pulse theory is shown to emerge as a limit of the more general formulation. Extensive simulations examine the role of the new solitons as robust attractors.

Citation

I. Bright Kerr solitons and cnoidal waves. Physical Review A, 86(2), 023838. https://doi.org/10.1103/PhysRevA.86.023838

• Journal Article Type: Article
• Publication Date: Jan 1, 2012
• Deposit Date: Oct 5, 2012
• Publicly Available Date: Oct 5, 2012
• Journal: Physical Review A
• Print ISSN: 1050-2947
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 86
• Issue: 2
• Pages: 023838
• DOI: https://doi.org/10.1103/PhysRevA.86.023838
• Publisher URL: http://link.aps.org/doi/10.1103/PhysRevA.86.023838