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

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

doi:10.1016/j.matcom.2005.03.017

Cited by 27 publications

(41 citation statements)

References 61 publications

(67 reference statements)

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“…The above, generalizes the well-known result 64 that the center of a dark soliton (the 1D "sibling" of the vortex) behaves like a Newtonian particle in the presence of the external potential (see relevant work for dark matter-wave solitons in optical lattices in Ref. [65]). Figure 3 depicts the vortex stability for the two detuning cases in (13).…”

Section: Continuum Modelssupporting

confidence: 81%

Vortices in Bose–einstein Condensates: Some Recent Developments

2004

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In this brief review we summarize a number of recent developments in the study of vortices in Bose-Einstein condensates, a topic of considerable theoretical and experimental interest in the past few years. We examine the generation of vortices by means of phase imprinting, as well as via dynamical instabilities. Their stability is subsequently examined in the presence of purely magnetic trapping, and in the combined presence of magnetic and optical trapping. We then study pairs of vortices and their interactions, illustrating a reduced description in terms of ordinary differential equations for the vortex centers. In the realm of two vortices we also consider the existence of stable dipole clusters for two-component condensates. Last but not least, we discuss mesoscopic patterns formed by vortices, the so-called vortex lattices and analyze some of their intriguing dynamical features. A number of interesting future directions are highlighted.

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Section: Continuum Modelssupporting

confidence: 81%

Vortices in Bose–einstein Condensates: Some Recent Developments

2004

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“…This can presumably be attributed to the emerging competition between the length scale of the lattice and that of the soliton proper (see the discussion in Ref. [50]), which contributes towards the decreased accuracy of the dark-soliton perturbation theory for moderate values of k.…”

Section: The Accuracy Of Analytical Approximationsmentioning

confidence: 99%

“…The steps of our analysis, and the structure of our presentation, are as follows. First, starting from a DGPE which encompasses the above potentials (linear and periodic), we employ two different analytical approaches: dark-soliton perturbation theory [2,[48][49][50] and the so-called Landau dynamics approach [51,52]; both analytical techniques lead to an equation of motion for the ensuing dynamics of the soliton center position (Sec. II).…”

Section: Introductionmentioning

confidence: 99%

Finite-temperature dynamics of matter-wave dark solitons in linear and periodic potentials: An example of an antidamped Josephson junction

et al. 2012

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We study matter-wave dark solitons in atomic Bose-Einstein condensates (BECs) at finite temperatures, under the effect of linear and periodic potentials. Our model, namely, a dissipative Gross-Pitaevskii equation, is treated analytically by means of dark-soliton perturbation theory and the Landau dynamics approach, which result in a Newtonian equation of motion for the dark-soliton center. This reduced model, which incorporates an effective washboard potential and an antidamping term accounting for finite-temperature effects, constitutes an example of an antidamped Josephson junction. We perform a qualitative (local and global) analysis of the equation of motion. We present results of systematic numerical simulations for both zero-and finite-temperature BECs to highlight the differences between the Hamiltonian and dissipative settings. For sufficiently small wave numbers of the periodic potential and weak linear potentials, the analytical results are found to be in good agreement with pertinent ones obtained via a Bogoliubov-de Gennes analysis and direct numerical simulations.

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“…We want to acknowledge V.V. Konotop for discussions and an anonymous referee for providing the reference [22].…”

Section: Acknowledgementsmentioning

confidence: 99%

Existence of Dark Soliton Solutions of the Cubic Nonlinear Schrödinger Equation with Periodic Inhomogeneous Nonlinearity

Belmonte-Beitia¹,

Torres²

2008

JNMP

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

Cited by 27 publications

References 61 publications

Vortices in Bose–einstein Condensates: Some Recent Developments

Vortices in Bose–einstein Condensates: Some Recent Developments

Finite-temperature dynamics of matter-wave dark solitons in linear and periodic potentials: An example of an antidamped Josephson junction

Existence of Dark Soliton Solutions of the Cubic Nonlinear Schrödinger Equation with Periodic Inhomogeneous Nonlinearity

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