Dark soliton dynamics in spatially inhomogeneous media: Application to Bose-Einstein condensates

G. Theocharis; D. J. Frantzeskakis; P. G. Kevrekidis; R. Carretero-González; B. A. Malomed

doi:10.1016/j.matcom.2005.03.017

Dark soliton dynamics in spatially inhomogeneous media: Application to Bose-Einstein condensates

G. Theocharis, D. J. Frantzeskakis, P. G. Kevrekidis, R. Carretero-González^*, B. A. Malomed

^*Corresponding author for this work

School of Electrical Engineering

Research output: Contribution to journal › Conference article › peer-review

25 Scopus citations

Abstract

We study the dynamics of dark solitons in spatially inhomogeneous media with applications to cigar-shaped Bose-Einstein condensates trapped in a harmonic magnetic potential and a periodic potential representing an optical lattice. We distinguish and systematically investigate the cases with the optical lattice period being smaller, larger, or comparable to the width of the dark soliton. Analytical results, based on perturbation techniques, for the motion of the dark soliton are obtained and compared to direct numerical simulations. Radiation effects are also considered. Finally, we demonstrate that a moving optical lattice may capture and drag a dark soliton.

Original language	English
Pages (from-to)	537-552
Number of pages	16
Journal	Mathematics and Computers in Simulation
Volume	69
Issue number	5-6
DOIs	https://doi.org/10.1016/j.matcom.2005.03.017
State	Published - 5 Aug 2005
Event	Nonlinear Waves: Computation and Theory IV - Duration: 7 Apr 2003 → 10 Apr 2003

Funding

Funders	Funder number
U.S. Air Force
San Diego State University
Eppley Foundation for Research	NSF-DMS-0204585
British Academy of Management
European Office of Aerospace Research and Development
United States-Israel Binational Science Foundation	1999459
John S. Latsis Public Benefit Foundation
National and Kapodistrian University of Athens	70/4/5844

Keywords

Bose-Einstein condensation
Matter waves
Optical lattice
Soliton

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10.1016/j.matcom.2005.03.017

Cite this

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title = "Dark soliton dynamics in spatially inhomogeneous media: Application to Bose-Einstein condensates",

abstract = "We study the dynamics of dark solitons in spatially inhomogeneous media with applications to cigar-shaped Bose-Einstein condensates trapped in a harmonic magnetic potential and a periodic potential representing an optical lattice. We distinguish and systematically investigate the cases with the optical lattice period being smaller, larger, or comparable to the width of the dark soliton. Analytical results, based on perturbation techniques, for the motion of the dark soliton are obtained and compared to direct numerical simulations. Radiation effects are also considered. Finally, we demonstrate that a moving optical lattice may capture and drag a dark soliton.",

keywords = "Bose-Einstein condensation, Matter waves, Optical lattice, Soliton",

author = "G. Theocharis and Frantzeskakis, {D. J.} and Kevrekidis, {P. G.} and R. Carretero-Gonz{\'a}lez and Malomed, {B. A.}",

note = "Funding Information: This work was supported by the “A.S. Onasis” Public Benefit Foundation (GT), the Special Research Account of the University of Athens, under grant no. 70/4/5844 (GT, DJF), a UMass FRG, the Eppley Foundation for Research and NSF-DMS-0204585 (PGK), the Binational (US-Israel) Science Foundation, under grant no. 1999459, and the European Office of Aerospace Research and Development of the US Air Force (BAM), and San Diego State University Foundation (RCG). Constructive discussions with N.P. Proukakis are kindly acknowledged.; Nonlinear Waves: Computation and Theory IV ; Conference date: 07-04-2003 Through 10-04-2003",

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T1 - Dark soliton dynamics in spatially inhomogeneous media

T2 - Nonlinear Waves: Computation and Theory IV

AU - Theocharis, G.

AU - Frantzeskakis, D. J.

AU - Kevrekidis, P. G.

AU - Carretero-González, R.

AU - Malomed, B. A.

N1 - Funding Information: This work was supported by the “A.S. Onasis” Public Benefit Foundation (GT), the Special Research Account of the University of Athens, under grant no. 70/4/5844 (GT, DJF), a UMass FRG, the Eppley Foundation for Research and NSF-DMS-0204585 (PGK), the Binational (US-Israel) Science Foundation, under grant no. 1999459, and the European Office of Aerospace Research and Development of the US Air Force (BAM), and San Diego State University Foundation (RCG). Constructive discussions with N.P. Proukakis are kindly acknowledged.

PY - 2005/8/5

Y1 - 2005/8/5

N2 - We study the dynamics of dark solitons in spatially inhomogeneous media with applications to cigar-shaped Bose-Einstein condensates trapped in a harmonic magnetic potential and a periodic potential representing an optical lattice. We distinguish and systematically investigate the cases with the optical lattice period being smaller, larger, or comparable to the width of the dark soliton. Analytical results, based on perturbation techniques, for the motion of the dark soliton are obtained and compared to direct numerical simulations. Radiation effects are also considered. Finally, we demonstrate that a moving optical lattice may capture and drag a dark soliton.

AB - We study the dynamics of dark solitons in spatially inhomogeneous media with applications to cigar-shaped Bose-Einstein condensates trapped in a harmonic magnetic potential and a periodic potential representing an optical lattice. We distinguish and systematically investigate the cases with the optical lattice period being smaller, larger, or comparable to the width of the dark soliton. Analytical results, based on perturbation techniques, for the motion of the dark soliton are obtained and compared to direct numerical simulations. Radiation effects are also considered. Finally, we demonstrate that a moving optical lattice may capture and drag a dark soliton.

KW - Bose-Einstein condensation

KW - Matter waves

KW - Optical lattice

KW - Soliton

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Y2 - 7 April 2003 through 10 April 2003

ER -

Dark soliton dynamics in spatially inhomogeneous media: Application to Bose-Einstein condensates

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