7,049 research outputs found
Reflection of Channel-Guided Solitons at Junctions in Two-Dimensional Nonlinear Schroedinger Equation
Solitons confined in channels are studied in the two-dimensional nonlinear
Schr\"odinger equation. We study the dynamics of two channel-guided solitons
near the junction where two channels are merged. The two solitons merge into
one soliton, when there is no phase shift. If a phase difference is given to
the two solitons, the Josephson oscillation is induced. The Josephson
oscillation is amplified near the junction. The two solitons are reflected when
the initial velocity is below a critical value.Comment: 3 pages, 2 figure
Cooperative jump motions of jammed particles in a one-dimensional periodic potential
Cooperative jump motions are studied for mutually interacting particles in a
one-dimensional periodic potential. The diffusion constant for the cooperative
motion in systems including a small number of particles is numerically
calculated and it is compared with theoretical estimates. We find that the size
distribution of the cooperative jump motions obeys an exponential law in a
large system.Comment: 5 pages, 4 figure
Higher-order vortex solitons, multipoles, and supervortices on a square optical lattice
We predict new generic types of vorticity-carrying soliton complexes in a
class of physical systems including an attractive Bose-Einstein condensate in a
square optical lattice (OL) and photonic lattices in photorefractive media. The
patterns include ring-shaped higher-order vortex solitons and supervortices.
Stability diagrams for these patterns, based on direct simulations, are
presented. The vortex ring solitons are stable if the phase difference \Delta
\phi between adjacent solitons in the ring is larger than \pi/2, while the
supervortices are stable in the opposite case, \Delta \phi <\pi /2. A
qualitative explanation to the stability is given.Comment: 9 pages, 4 figure
Galilean Superconformal Symmetries
We consider the non-relativistic c -> \infty contraction limit of the (N=2k)-
extended D=4 superconformal algebra su(2,2;N), introducing in this way the
non-relativistic (N=2k)-extended Galilean superconformal algebra. Such a
Galilean superconformal algebra has the same number of generators as
su(2,2|2k). The usp(2k) algebra describes the non-relativistic internal
symmetries, and the generators from the coset u(2k)/usp(2k) become central
charges after contraction.Comment: 15 pages; v3:2 reference added, misprints corrected. Version to
appear in PL
Instability of synchronized motion in nonlocally coupled neural oscillators
We study nonlocally coupled Hodgkin-Huxley equations with excitatory and
inhibitory synaptic coupling. We investigate the linear stability of the
synchronized solution, and find numerically various nonuniform oscillatory
states such as chimera states, wavy states, clustering states, and
spatiotemporal chaos as a result of the instability.Comment: 8 pages, 9 figure
Localized matter-waves patterns with attractive interaction in rotating potentials
We consider a two-dimensional (2D) model of a rotating attractive
Bose-Einstein condensate (BEC), trapped in an external potential. First, an
harmonic potential with the critical strength is considered, which generates
quasi-solitons at the lowest Landau level (LLL). We describe a family of the
LLL quasi-solitons using both numerical method and a variational approximation
(VA), which are in good agreement with each other. We demonstrate that kicking
the LLL mode or applying a ramp potential sets it in the Larmor (cyclotron)
motion, that can also be accurately modeled by the VA.Comment: 13 pages, 11 figure
Solitons in combined linear and nonlinear lattice potentials
We study ordinary solitons and gap solitons (GSs) in the effectively
one-dimensional Gross-Pitaevskii equation, with a combination of linear and
nonlinear lattice potentials. The main points of the analysis are effects of
the (in)commensurability between the lattices, the development of analytical
methods, viz., the variational approximation (VA) for narrow ordinary solitons,
and various forms of the averaging method for broad solitons of both types, and
also the study of mobility of the solitons. Under the direct commensurability
(equal periods of the lattices, the family of ordinary solitons is similar to
its counterpart in the free space. The situation is different in the case of
the subharmonic commensurability, with L_{lin}=(1/2)L_{nonlin}, or
incommensurability. In those cases, there is an existence threshold for the
solitons, and the scaling relation between their amplitude and width is
different from that in the free space. GS families demonstrate a bistability,
unless the direct commensurability takes place. Specific scaling relations are
found for them too. Ordinary solitons can be readily set in motion by kicking.
GSs are mobile too, featuring inelastic collisions. The analytical
approximations are shown to be quite accurate, predicting correct scaling
relations for the soliton families in different cases. The stability of the
ordinary solitons is fully determined by the VK (Vakhitov-Kolokolov) criterion,
while the stability of GS families follows an inverted ("anti-VK") criterion,
which is explained by means of the averaging approximation.Comment: 9 pages, 6 figure
Nondegenerate Super-Anti-de Sitter Algebra and a Superstring Action
We construct an Anti-de Sitter(AdS) algebra in a nondegenerate superspace.
Based on this algebra we construct a covariant kappa-symmetric superstring
action, and we examine its dynamics: Although this action reduces to the usual
Green-Schwarz superstring action in flat limit, the auxiliary fermionic
coordinates of the nondegenerate superspace becomes dynamical in the AdS
background.Comment: Latex, 12 pages, explanations added, version to be published in Phys.
Rev.
Gap solitons in Bragg gratings with a harmonic superlattice
Solitons are studied in a model of a fiber Bragg grating (BG) whose local
reflectivity is subjected to periodic modulation. The superlattice opens an
infinite number of new bandgaps in the model's spectrum. Averaging and
numerical continuation methods show that each gap gives rise to gap solitons
(GSs), including asymmetric and double-humped ones, which are not present
without the superlattice.Computation of stability eigenvalues and direct
simulation reveal the existence of completely stable families of fundamental
GSs filling the new gaps - also at negative frequencies, where the ordinary GSs
are unstable. Moving stable GSs with positive and negative effective mass are
found too.Comment: 7 pages, 3 figures, submitted to EP
Gap solitons in quasiperiodic optical lattices
Families of solitons in one- and two-dimensional (1D and 2D) Gross-Pitaevskii
equations with the repulsive nonlinearity and a potential of the
quasicrystallic type are constructed (in the 2D case, the potential corresponds
to a five-fold optical lattice). Stable 1D solitons in the weak potential are
explicitly found in three bandgaps. These solitons are mobile, and they collide
elastically. Many species of tightly bound 1D solitons are found in the strong
potential, both stable and unstable (unstable ones transform themselves into
asymmetric breathers). In the 2D model, families of both fundamental and
vortical solitons are found and are shown to be stable.Comment: 8 pages, 11 figure
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