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

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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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
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: 15 Feb 2022 16:24
URI: https://usir.salford.ac.uk/id/eprint/26905

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