Propagation of matter-wave solitons in periodic and random nonlinear potentials

Abdullaev, F. Kh.; Garnier, Josselin

doi:10.1103/physreva.72.061605

Cited by 109 publications

(93 citation statements)

References 21 publications

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“…This possibility has motivated in the last years a strong theoretical interest on nonlinear phenomena in Bose-Eintein condensates (BECs) with spatially inhomogeneous interactions. Several phenomena have been studied in quasi-one dimensional scenarios such as the emission of solitons [12] and the dynamics of solitons when the space modulation of the nonlinearity is a random [14], linear [15], periodic [16], or localized function [17]. The existence and stability of solutions has been studied in Ref.…”

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confidence: 99%

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Lie Symmetries and Solitons in Nonlinear Systems with Spatially Inhomogeneous Nonlinearities

et al. 2007

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Using Lie group theory and canonical transformations we construct explicit solutions of nonlinear Schrödinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to show that localized nonlinearities can support bound states with an arbitrary number solitons and discuss other applications of interest to the field of nonlinear matter waves. Introduction.-Solitons are self-localized nonlinear waves which are sustained by an equilibrium between dispersion and nonlinearity and appear in a great variety of physical contexts [1]. In particular, these nonlinear structures have been generated recently in ultracold atomic bosonic gases cooled down below the Bose-Einstein transition temperature [2,3,4]. In those systems the effective nonlinear interactions are a result of the elastic two-body collisions between the condensed atoms.These interactions can be controlled by the so-called Feschbach resonance (FR) management [5], which has been used to generate bright solitons [3,6], induce collapse [7], etc. Recently, the control in time of the condensate scattering length has been the basis for many theoretical proposals to obtain different types of nonlinear structures such as periodic waves [8], shock waves [9], stabilized solitons [10], etc.Interactions can also be made spatially dependent by acting on the spatial dependence of either the magnetic field or the laser intensity (in the case of optical control of FR [11]) acting on the Feschbach resonances. This possibility has motivated in the last years a strong theoretical interest on nonlinear phenomena in Bose-Eintein condensates (BECs) with spatially inhomogeneous interactions. Several phenomena have been studied in quasi-one dimensional scenarios such as the emission of solitons [12] and the dynamics of solitons when the space modulation of the nonlinearity is a random [14], linear [15], periodic [16], or localized function [17]. The existence and stability of solutions has been studied in Ref. [18].In this paper we construct general classes of nonlinearity modulations and external potentials for which explicit solutions can be constructed. To do so we will use Lie group theory and canonical tranformations connecting problems with inhomogeneous nonlinearities with simpler ones having an homogeneous nonlinearity. We will show that localized nonlinearities can support bound

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confidence: 99%

“…Thus, given any arbitrary solution of the linear Schrödinger equation (14) we can construct solutions of the nonlinear spatially inhomogeneous problem Eq. (2) from the known solutions of Eq.…”

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confidence: 99%

Lie Symmetries and Solitons in Nonlinear Systems with Spatially Inhomogeneous Nonlinearities

et al. 2007

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“…(38)(39)(40)(41). To this end, we set ζ = ζ s + δζ, δζ ≪ ζ s , where ζ s is the fixed point, and a = a s + δa, δa ≪ a.…”

Section: Dynamics Of Bright Solitonsmentioning

confidence: 99%

“…The soliton motion in nonlinear lattices was previously considered in Refs. [40,41,42,43]. First, we present full numerical solutions of the 1D GPE (8), exploring a parameter region for finding stable bright-solitons solutions.…”

Section: Dynamics Of Bright Solitonsmentioning

confidence: 99%

Bright solitons in Bose–Einstein condensates with field-induced dipole moments

Abdullaev

Gammal

Malomed

et al. 2014

J. Phys. B: At. Mol. Opt. Phys.

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Abstract. We introduce an effectively one-dimensional (1D) model of a bosonic gas of particles carrying collinear dipole moments which are induced by an external polarizing field with the strength periodically modulated along the coordinate, which gives rise to an effective nonlocal nonlinear lattice in the condensate. The existence, shape and stability of bright solitons, appearing in this model, are investigated by means of the variational approximation and numerical methods. The mobility of solitons and interactions between them are studied too.

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“…Moreover, interactions can be made spatially dependent by acting on either the spatial dependence of the magnetic field or the laser intensity (in the case of optical control of FRs [19]) which act on the Feschbach resonances. This possibility has motivated many theoretical studies on the behavior of solitons in Bose-Einstein condensates (BECs) with spatially inhomogeneous interactions [20,21,22,23,24,25,26,27,28,29,30,31,32,33,34].…”

Section: Introductionmentioning

confidence: 99%

Localization phenomena in nonlinear Schrödinger equations with spatially inhomogeneous nonlinearities: Theory and applications to Bose–Einstein condensates

Pérez-Garcı́a

Pardo

2009

Physica D: Nonlinear Phenomena

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We study the properties of the ground state of Nonlinear Schrödinger Equations with spatially inhomogeneous interactions and show that it experiences a strong localization on the spatial region where the interactions vanish. At the same time, tunneling to regions with positive values of the interactions is strongly supressed by the nonlinear interactions and as the number of particles is increased it saturates in the region of finite interaction values. The chemical potential has a cutoff value in these systems and thus takes values on a finite interval. The applicability of the phenomenon to Bose-Einstein condensates is discussed in detail.

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Propagation of matter-wave solitons in periodic and random nonlinear potentials

Cited by 109 publications

References 21 publications

Lie Symmetries and Solitons in Nonlinear Systems with Spatially Inhomogeneous Nonlinearities

Lie Symmetries and Solitons in Nonlinear Systems with Spatially Inhomogeneous Nonlinearities

Bright solitons in Bose–Einstein condensates with field-induced dipole moments

Localization phenomena in nonlinear Schrödinger equations with spatially inhomogeneous nonlinearities: Theory and applications to Bose–Einstein condensates

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