| 1. |
- Johansson, Magnus, et al.
(författare)
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Comment on "localized vortices with a semi-integer charge in nonlinear dynamical lattices"
- 2002
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Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics. - 1539-3755 .- 1550-2376. ; 66:4, s. 048601-
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- In a recent paper by Kevrekidis, Malomed, Bishop, and Frantzeskakis [Phys. Rev. E 65, 016605 (2001)] the existence of localized vortices with semi-integer topological charge as exact stationary solutions in a two-dimensional discrete nonlinear Schrödinger model is claimed, as well as the existence of an analog solution in the one-dimensional model. We point out that the existence of such exact stationary solutions would violate fundamental conservation laws, and therefore these claims are erroneous and appear as a consequence of inaccurate numerics. We illustrate the origin of these errors by performing similar numerical calculations using more accurate numerics.
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| 2. |
- Kevrekidis, P. G., et al.
(författare)
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Adiabatic invariant analysis of dark and dark-bright soliton stripes in two-dimensional Bose-Einstein condensates
- 2018
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Ingår i: Physical Review A: covering atomic, molecular, and optical physics and quantum information. - : American Physical Society. - 2469-9926 .- 2469-9934. ; 97:6
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Tidskriftsartikel (refereegranskat)abstract
- In the present work, we develop an adiabatic invariant approach for the evolution of quasi-one-dimensional (stripe) solitons embedded in a two-dimensional Bose-Einstein condensate. The results of the theory are obtained both for the one-component case of dark soliton stripes, as well as for the considerably more involved case of the two-component dark-bright (alias "filled dark") soliton stripes. In both cases, analytical predictions regarding the stability and dynamics of these structures are obtained. One of our main findings is the determination of the instability modes of the waves as a function of the parameters of the system (such as the trap strength and the chemical potential). Our analytical predictions are favorably compared with results of direct numerical simulations.
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| 3. |
- Kevrekidis, P. G., et al.
(författare)
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Dynamics of interacting dark soliton stripes
- 2019
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Ingår i: Physical Review A: covering atomic, molecular, and optical physics and quantum information. - : AMER PHYSICAL SOC. - 2469-9926 .- 2469-9934. ; 100:3
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Tidskriftsartikel (refereegranskat)abstract
- In the present work we examine the statics and dynamics of multiple parallel dark soliton stripes in a two-dimensional Bose-Einstein condensate. Our principal goal is to study the effect of the interaction between the stripes on the transverse instability of the individual stripes. The cases of two-, three-, and four-stripe states are studied in detail. We use a recently developed adiabatic invariant formulation to derive a quasianalytical prediction for the stripe equilibrium position and for the Bogoliubov-de Gennes spectrum of excitations of stationary stripes. We subsequently test our predictions against numerical simulations of the full two-dimensional Gross-Pitaevskii equation. We find that the number of unstable eigenmodes increases as the number of stripes increases due to (unstable) relative motions between the stripes. Their corresponding growth rates do not significantly change, although for large chemical potentials, the larger the stripe number, the larger the maximal instability growth rate. The instability induced dynamics of multiple stripe states and their decay into vortices are also investigated.
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