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 :
I. Bright Kerr solitons and cnoidal waves'
, Physical Review A, 86 (2)
, 023838.
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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.
Item Type: | Article |
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Themes: | Subjects outside of the University Themes |
Schools: | Schools > School of Computing, Science and Engineering > Salford Innovation Research Centre |
Journal or Publication Title: | Physical Review A |
Publisher: | American Physical Society |
Refereed: | Yes |
ISSN: | 1050-2947 |
Depositing User: | JM Christian |
Date Deposited: | 05 Oct 2012 14:22 |
Last Modified: | 28 Oct 2020 13:33 |
URI: | http://usir.salford.ac.uk/id/eprint/26905 |
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