3,336 research outputs found
An Adiabatic Invariant Approach to Transverse Instability: Landau Dynamics of Soliton Filaments
Assume a lower-dimensional solitonic structure embedded in a higher
dimensional space, e.g., a 1D dark soliton embedded in 2D space, a ring dark
soliton in 2D space, a spherical shell soliton in 3D space etc. By extending
the Landau dynamics approach [Phys. Rev. Lett. {\bf 93}, 240403 (2004)], we
show that it is possible to capture the transverse dynamical modes (the "Kelvin
modes") of the undulation of this "soliton filament" within the higher
dimensional space. These are the transverse stability/instability modes and are
the ones potentially responsible for the breakup of the soliton into structures
such as vortices, vortex rings etc. We present the theory and case examples in
2D and 3D, corroborating the results by numerical stability and dynamical
computations.Comment: 5 pages, 3 figure
Exploring Vortex Dynamics in the Presence of Dissipation: Analytical and Numerical Results
In this paper, we systematically examine the stability and dynamics of
vortices under the effect of a phenomenological dissipation used as a
simplified model for the inclusion of the effect of finite temperatures in
atomic Bose-Einstein condensates. An advantage of this simplified model is that
it enables an analytical prediction that can be compared directly (and
favorably) to numerical results. We then extend considerations to a case of
considerable recent experimental interest, namely that of a vortex dipole and
observe good agreement between theory and numerical computations in both the
stability properties (eigenvalues of the vortex dipole stationary states) and
the dynamical evolution of such configurations.Comment: 12 pages, 5 figures, accepted by PR
Three-Dimensional Nonlinear Lattices: From Oblique Vortices and Octupoles to Discrete Diamonds and Vortex Cubes
We construct a variety of novel localized states with distinct topological
structures in the 3D discrete nonlinear Schr{\"{o}}dinger equation. The states
can be created in Bose-Einstein condensates trapped in strong optical lattices,
and crystals built of microresonators. These new structures, most of which have
no counterparts in lower dimensions, range from purely real patterns of dipole,
quadrupole and octupole types to vortex solutions, such as "diagonal" and
"oblique" vortices, with axes oriented along the respective directions
and . Vortex "cubes" (stacks of two quasi-planar vortices
with like or opposite polarities) and "diamonds" (discrete skyrmions formed by
two vortices with orthogonal axes) are constructed too. We identify stability
regions of these 3D solutions and compare them with their 2D counterparts, if
any. An explanation for the stability/instability of most solutions is
proposed. The evolution of unstable states is studied as well.Comment: 4 pages, 4 figures, submitted January 200
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