Two-dimensional nonlocal multisolitons

Lashkin, Volodymyr M.; Yakimenko, A. I.; Prikhodko, O. O.

doi:10.1016/j.physleta.2007.02.042

Cited by 31 publications

(24 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In contrast to the linear vortex phase, the phase of the azimuthon is a staircaselike nonlinear function of the polar angle. Various kinds of azimuthons have been shown to be stable in media with a nonlocal nonlinear response [7,8,9,10,11].The aim of this Brief Report is to present nonrotating multisoliton (in particular, dipole and quadrupole) and rotating multisoliton (azimuthon) structures in the 2D BEC with attraction and study their stability by a linear stability analysis. We show that, in the presence of a confining potential, stable azimuthons also exist for a medium with a local cubic attractive nonlinearity.…”

mentioning

confidence: 99%

Two-dimensional multisolitons and azimuthons in Bose-Einstein condensates

Lashkin

2008

Phys. Rev. A

View full text Add to dashboard Cite

We present spatially localized nonrotating and rotating (azimuthon) multisolitons in the twodimensional (2D) ("pancake-shaped configuration") Bose-Einstein condensate (BEC) with attractive interaction. By means of a linear stability analysis, we investigate the stability of these structures and show that rotating dipole solitons are stable provided that the number of atoms is small enough. The results were confirmed by direct numerical simulations of the 2D Gross-Pitaevskii equation.PACS numbers: 03.75. Lm, 05.30.Jp, 05.45.Yv Localized coherent structures, such as fundamental solitons, vortices, nonrotating and rotating multisolitons are universal objects which appear in many nonlinear physical systems [1], and, in particular, in Bose-Einstein condensates (BEC's). Stability of these nonlinear structures is one of the most important questions because of its direct connection with the possibility of experimental observation of solitons and vortices.Detailed investigations of the stability of localized vortices in an effectively two-dimensional (2D) trapped BEC with a negative scattering length (attractive interaction) were performed in Ref.[2] and later extended to the three-dimensional case [3] (see also Ref. [4]). While vortex solitons in attractive BEC are strongly unstable in free space, the presence of the trapping potential results in existence of stable vortices provided that the number of particles does not exceed a threshold value [2,4,5].Recently, a novel class of 2D spatially localized vortices with a spatially modulated phase, the so called azimuthons, was introduced in Ref. [6]. Azimuthons represent intermediate states between the radially symmetric vortices and rotating soliton clusters. In contrast to the linear vortex phase, the phase of the azimuthon is a staircaselike nonlinear function of the polar angle. Various kinds of azimuthons have been shown to be stable in media with a nonlocal nonlinear response [7,8,9,10,11].The aim of this Brief Report is to present nonrotating multisoliton (in particular, dipole and quadrupole) and rotating multisoliton (azimuthon) structures in the 2D BEC with attraction and study their stability by a linear stability analysis. We show that, in the presence of a confining potential, stable azimuthons also exist for a medium with a local cubic attractive nonlinearity. Results of the linear stability analysis were confirmed by direct numerical simulations of the azimuthon dynamics.We consider a condensate which is loaded in an axisymmetric with respect to the (x, y) plane harmonic trap, and tightly confined in the z direction. The dynamics of the condensate is described by the Gross-Pitaevskii equation * Electronic address: vlashkin@kinr.kiev.uawhere Ψ(r, t) is the condensate wave function, a ≷ 0 is the s-wave scattering length. We assume that the axial confinement frequency Ω z is much larger than the radial one Ω r (the pancake configuration). Then, the 3D equation (1) can be reduced to an effective GPE in two dimensions [2] (for a detailed discussion of the appl...

show abstract

mentioning

confidence: 99%

Two-dimensional multisolitons and azimuthons in Bose-Einstein condensates

Lashkin

2008

Phys. Rev. A

View full text Add to dashboard Cite

show abstract

“…As was demonstrated recently, stable rotating azimuthons become possible when the nonlocality parameter exceeds a certain threshold value [10,11]. The simplest example of such multipole solitons is a dipole-like structure composed of two interacting fundamental beams with the opposite phases that undergo angular rotation during the propagation [12,13,14].…”

Section: Introductionmentioning

confidence: 88%

Vortex Solitons and Rotating Azimuthons in Nonlinear Media

Desyatnikov

Kivshar

2009

Topologica

View full text Add to dashboard Cite

We give a brief overview of the recent advances in nonlinear singular optics that studies the propagation and stability of optical vortices in nonlinear media, with the emphasis on the properties of vortex solitons and rotating azimuthons. In general, self-focusing nonlinearity generates the azimuthal instability of vortex beams, but it can support novel types of stable (or metastable) self-trapped beams with a finite angular momentum, such as ring-like necklace beams and soliton clusters. In particular, we describe azimuthons and multi-vortex solitons which provide the generalization of the LaguerreGaussian and Hermite-Gaussian optical beams and demonstrate that many of such vortex-carrying beams can be stabilized in the media with nonlocal nonlinear response.

show abstract

“…In sharp contrast to the case of local media, where multipole solitons tend to be dynamically unstable, except in the form of vector solitons under suitable conditions, out-of-phase bright solitons can attract each other and may even form scalar bound states, in both one- [22,23] and two dimensional [24][25][26][27][28][29][30] geometries in nonlocal nonlinear media. Stationary 2D dipole-mode solitons have been observed experimentally in media with the thermal nonlinearity [24].…”

Section: Introductionmentioning

confidence: 89%

“…Dipole-mode solitons [19][20][21], comprising two out-of-phase peaks packed together by the force acting between them, attracted much attention in nonlocal nonlinear media [22][23][24][25][26][27][28][29][30]. In sharp contrast to the case of local media, where multipole solitons tend to be dynamically unstable, except in the form of vector solitons under suitable conditions, out-of-phase bright solitons can attract each other and may even form scalar bound states, in both one- [22,23] and two dimensional [24][25][26][27][28][29][30] geometries in nonlocal nonlinear media.…”

Section: Introductionmentioning

confidence: 99%