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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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
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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