Wave envelopes with second-order spatiotemporal dispersion : I. Bright Kerr solitons and cnoidal waves
Christian, J M, McDonald, G S, 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.
|Themes:||Subjects outside of the University Themes|
|Schools:||Schools > School of Computing, Science and Engineering > Salford Innovation Research Centre (SIRC)|
|Journal or Publication Title:||Physical Review A|
|Publisher:||American Physical Society|
|Depositing User:||JM Christian|
|Date Deposited:||05 Oct 2012 14:22|
|Last Modified:||29 Oct 2015 00:10|
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