685 research outputs found

### Matter-wave solitons in radially periodic potentials

We investigate two-dimensional (2D) states of Bose-Einstein condensates (BEC)
with self-attraction or self-repulsion, trapped in an axially symmetric
optical-lattice potential periodic along the radius. Unlike previously studied
2D models with Bessel lattices, no localized states exist in the linear limit
of the present model, hence all localized states are truly nonlinear ones. We
consider the states trapped in the central potential well, and in remote
circular troughs. In both cases, a new species, in the form of \textit{radial
gap solitons}, are found in the repulsive model (the gap soliton trapped in a
circular trough may additionally support stable dark-soliton pairs). In remote
troughs, stable localized states may assume a ring-like shape, or shrink into
strongly localized solitons. The existence of stable annular states, both
azimuthally uniform and weakly modulated ones, is corroborated by simulations
of the corresponding Gross-Pitaevskii equation. Dynamics of strongly localized
solitons circulating in the troughs is also studied. While the solitons with
sufficiently small velocities are stable, fast solitons gradually decay, due to
the leakage of matter into the adjacent trough under the action of the
centrifugal force. Collisions between solitons are investigated too. Head-on
collisions of in-phase solitons lead to the collapse; $\pi$-out of phase
solitons bounce many times, but eventually merge into a single soliton without
collapsing. The proposed setting may also be realized in terms of spatial
solitons in photonic-crystal fibers with a radial structure.Comment: 16 pages, 23 figure

### Dragging two-dimensional discrete solitons by moving linear defects

We study the mobility of small-amplitude solitons attached to moving defects
which drag the solitons across a two-dimensional (2D) discrete
nonlinear-Schr\"{o}dinger (DNLS) lattice. Findings are compared to the
situation when a free small-amplitude 2D discrete soliton is kicked in the
uniform lattice. In agreement with previously known results, after a period of
transient motion the free soliton transforms into a localized mode pinned by
the Peierls-Nabarro potential, irrespective of the initial velocity. However,
the soliton attached to the moving defect can be dragged over an indefinitely
long distance (including routes with abrupt turns and circular trajectories)
virtually without losses, provided that the dragging velocity is smaller than a
certain critical value. Collisions between solitons dragged by two defects in
opposite directions are studied too. If the velocity is small enough, the
collision leads to a spontaneous symmetry breaking, featuring fusion of two
solitons into a single one, which remains attached to either of the two
defects

### The ac-Driven Motion of Dislocations in a Weakly Damped Frenkel-Kontorova Lattice

By means of numerical simulations, we demonstrate that ac field can support
stably moving collective nonlinear excitations in the form of dislocations
(topological solitons, or kinks) in the Frenkel-Kontorova (FK) lattice with
weak friction, which was qualitatively predicted by Bonilla and Malomed [Phys.
Rev. B{\bf 43}, 11539 (1991)]. Direct generation of the moving dislocations
turns out to be virtually impossible; however, they can be generated initially
in the lattice subject to an auxiliary spatial modulation of the on-site
potential strength. Gradually relaxing the modulation, we are able to get the
stable moving dislocations in the uniform FK lattice with the periodic boundary
conditions, provided that the driving frequency is close to the gap frequency
of the linear excitations in the uniform lattice. The excitations have a large
and noninteger index of commensurability with the lattice (suggesting that its
actual value is irrational). The simulations reveal two different types of the
moving dislocations: broad ones, that extend, roughly, to half the full length
of the periodic lattice (in that sense, they cannot be called solitons), and
localized soliton-like dislocations, that can be found in an excited state,
demonstrating strong persistent internal vibrations. The minimum (threshold)
amplitude of the driving force necessary to support the traveling excitation is
found as a function of the friction coefficient. Its extrapolation suggests
that the threshold does not vanish at the zero friction, which may be explained
by radiation losses. The moving dislocation can be observed experimentally in
an array of coupled small Josephson junctions in the form of an {\it inverse
Josephson effect}, i.e., a dc-voltage response to the uniformly applied ac bias
current.Comment: Plain Latex, 13 pages + 9 PostScript figures. to appear on Journal of
Physics: condensed matte

### Two-component gap solitons with linear interconversion

We consider one-dimensional solitons in a binary Bose-Einstein condensate
with linear coupling between the components, trapped in an optical-lattice
potential. The inter-species and intra-species interactions may be both
repulsive or attractive. Main effects considered here are spontaneous breaking
of the symmetry between components in symmetric and antisymmetric solitons, and
spatial splitting between the components. These effects are studied by means of
a variational approximation and numerical simulations.Comment: 4 pages, 9 figure

### Bose-Einstein condensates under a spatially-modulated transverse confinement

We derive an effective nonpolynomial Schrodinger equation (NPSE) for
self-repulsive or attractive BEC in the nearly-1D cigar-shaped trap, with the
transverse confining frequency periodically modulated along the axial
direction. Besides the usual linear cigar-shaped trap, where the periodic
modulation emulates the action of an optical lattice (OL), the model may be
also relevant to toroidal traps, where an ordinary OL cannot be created. For
either sign of the nonlinearity, extended and localized states are found, in
the numerical form (using both the effective NPSE and the full 3D
Gross-Pitaevskii equation) and by means of the variational approximation (VA).
The latter is applied to construct ground-state solitons and predict the
collapse threshold in the case of self-attraction. It is shown that numerical
solutions provided by the one-dimensional NPSE are always very close to full 3D
solutions, and the VA yields quite reasonable results too. The transition from
delocalized states to gap solitons, in the first finite bandgap of the linear
spectrum, is examined in detail, for the repulsive and attractive
nonlinearities alike.Comment: 10 pages, 10 figures, accepted for publication in Phys. Rev.

### Multidimensional solitons in periodic potentials

The existence of stable solitons in two- and three-dimensional (2D and 3D)
media governed by the self-focusing cubic nonlinear Schr\"{o}dinger equation
with a periodic potential is demonstrated by means of the variational
approximation (VA) and in direct simulations. The potential stabilizes the
solitons against collapse. Direct physical realizations are a Bose-Einstein
condensate (BEC) trapped in an optical lattice, and a light beam in a bulk Kerr
medium of a photonic-crystal type. In the 2D case, the creation of the soliton
in a weak lattice potential is possible if the norm of the field (number of
atoms in BEC, or optical power in the Kerr medium) exceeds a threshold value
(which is smaller than the critical norm leading to collapse). Both
"single-cell" and "multi-cell" solitons are found, which occupy, respectively,
one or several cells of the periodic potential, depending on the soliton's
norm. Solitons of the former type and their stability are well predicted by VA.
Stable 2D vortex solitons are found too.Comment: 13 pages, 3 figures, Europhys. Lett., in pres

### Bright solitons from defocusing nonlinearities

We report that defocusing cubic media with spatially inhomogeneous
nonlinearity, whose strength increases rapidly enough toward the periphery, can
support stable bright localized modes. Such nonlinearity landscapes give rise
to a variety of stable solitons in all three dimensions, including 1D
fundamental and multihump states, 2D vortex solitons with arbitrarily high
topological charges, and fundamental solitons in 3D. Solitons maintain their
coherence in the state of motion, oscillating in the nonlinear potential as
robust quasi-particles and colliding elastically. In addition to numerically
found soliton families, particular solutions are found in an exact analytical
form, and accurate approximations are developed for the entire families,
including moving solitons.Comment: 13 pages, 6 figures, to appear in Physical Review

### Guiding-center solitons in rotating potentials

We demonstrate that rotating quasi-one-dimensional potentials, periodic or
parabolic, support solitons in settings where they are otherwise impossible.
Ground-state and vortex solitons are found in defocusing media, if the rotation
frequency exceeds a critical value. The revolving periodic potentials exhibit
the strongest stabilization capacity at a finite optimum value of their
strength, while the rotating parabolic trap features a very sharp transition to
stability with the increase of rotation frequency.Comment: 16 pages, 6 figures, to appear in Physical Review

### Quasi-one-dimensional Bose-Einstein condensates in nonlinear lattices

We consider the three-dimensional (3D) mean-field model for the Bose-Einstein
condensate (BEC), with a 1D nonlinear lattice (NL), which periodically changes
the sign of the nonlinearity along the axial direction, and the
harmonic-oscillator trapping potential applied in the transverse plane. The
lattice can be created as an optical or magnetic one, by means of available
experimental techniques. The objective is to identify stable 3D solitons
supported by the setting. Two methods are developed for this purpose: The
variational approximation, formulated in the framework of the 3D
Gross-Pitaevskii equation, and the 1D nonpolynomial Schr\"{o}dinger equation
(NPSE) in the axial direction, which allows one to predict the collapse in the
framework of the 1D description. Results are summarized in the form of a
stability region for the solitons in the plane of the NL strength and
wavenumber. Both methods produce a similar form of the stability region. Unlike
their counterparts supported by the NL in the 1D model with the cubic
nonlinearity, kicked solitons of the NPSE cannot be set in motion, but the kick
may help to stabilize them against the collapse, by causing the solitons to
shed excess norm. A dynamical effect specific to the NL is found in the form of
freely propagating small-amplitude wave packets emitted by perturbed solitons.Comment: 14 pages, 8 figures. To be published in J. Phys. B: At. Mol. Opt.
Phy

### Light Bullets in Nonlinear Periodically Curved Waveguide Arrays

We predict that stable mobile spatio-temporal solitons can exist in arrays of
periodically curved optical waveguides. We find two-dimensional light bullets
in one-dimensional arrays with harmonic waveguide bending and three-dimensional
bullets in square lattices with helical waveguide bending using variational
formalism. Stability of the light bullet solutions is confirmed by the direct
numerical simulations which show that the light bullets can freely move across
the curved arrays. This mobility property is a distinguishing characteristic
compared to previously considered discrete light bullets which were trapped to
a specific lattice site. These results suggest new possibilities for flexible
spatio-temporal manipulation of optical pulses in photonic lattices.Comment: 7 pages, 4 figure

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