Autoresonant excitation of dark solitons(Article)
- aInstitute of Metal Physics, Russian Federation and Ural Federal University, Mira 19, Ekaterinburg, 620002, Russian Federation
- bRacah Institute of Physics, Hebrew University of Jerusalem, Jerusalem, 91904, Israel
Abstract
Continuouslyphase-locked (autoresonant) dark solitons of the defocusing nonlinear Schrodinger equation are excited and controlled by driving the system by a slowly chirped wavelike perturbation. The theory of these excitations is developed using Whitham's averaged variational principle and compared with numerical simulations. The problem of the threshold for transition to autoresonance in the driven system is studied in detail, focusing on the regime when the weakly nonlinear frequency shift in the problem differs from the typical quadratic dependence on the wave amplitude. The numerical simulations in this regime show a deviation of the autoresonance threshold on the driving amplitude from the usual 3/4 power dependence on the driving frequency chirp rate. The theory of this effect is suggested. © 2015 American Physical Society.
Indexed keywords
| Engineering controlled terms: | Control nonlinearitiesNonlinear equationsNumerical modelsPerturbation techniquesSchrodinger equationVariational techniques |
|---|---|
| Engineering uncontrolled terms | Autoresonant excitationDriving frequenciesPower dependenceQuadratic dependenceVariational principlesWave amplitudesWavelike perturbationsWeakly non-linear |
| Engineering main heading: | Solitons |
Funding details
| Funding sponsor | Funding number | Acronym |
|---|---|---|
| 12-P-2-1045,451/10 |
- ISSN: 15393755
- CODEN: PLEEE
- Source Type: Journal
- Original language: English
- DOI: 10.1103/PhysRevE.91.012913
- Document Type: Article
- Publisher: American Physical Society
© Copyright 2015 Elsevier B.V., All rights reserved.
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