7,468 research outputs found
Darboux transformation and multi-soliton solutions of Two-Boson hierarchy
We study Darboux transformations for the two boson (TB) hierarchy both in the
scalar as well as in the matrix descriptions of the linear equation. While
Darboux transformations have been extensively studied for integrable models
based on within the AKNS framework, this model is based on
. The connection between the scalar and the matrix
descriptions in this case implies that the generic Darboux matrix for the TB
hierarchy has a different structure from that in the models based on
studied thus far. The conventional Darboux transformation is shown to be quite
restricted in this model. We construct a modified Darboux transformation which
has a much richer structure and which also allows for multi-soliton solutions
to be written in terms of Wronskians. Using the modified Darboux
transformations, we explicitly construct one soliton/kink solutions for the
model.Comment:
Vortices in attractive Bose-Einstein condensates in two dimensions
The form and stability of quantum vortices in Bose-Einstein condensates with
attractive atomic interactions is elucidated. They appear as ring bright
solitons, and are a generalization of the Townes soliton to nonzero winding
number . An infinite sequence of radially excited stationary states appear
for each value of , which are characterized by concentric matter-wave rings
separated by nodes, in contrast to repulsive condensates, where no such set of
states exists. It is shown that robustly stable as well as unstable regimes may
be achieved in confined geometries, thereby suggesting that vortices and their
radial excited states can be observed in experiments on attractive condensates
in two dimensions.Comment: 4 pages, 3 figure
Radial rotating antenna-feed system
System incorporating two or more radial feed assemblies tracks and communicates with multiple moving transmitters, receivers, or transponders. System utilizes a fixed parabolic reflector or other beam-forming device such as a lens or spherical reflector
Eddy-current inspection of shuttle heat exchanger tube welds
The goal of this project was to develop the system necessary to demonstrate in the laboratory that an eddy current system can inspect the tubes and welds described, screening for the existence of flaws equal in size to, or larger than, the target flaw. The laboratory system was to include the probe necessary to traverse the tubing, the electronics to drive (i.e., electrically excite) the probe and receive and process signals from it, a data display, data recording, and playback devices, and microprocessor software or firmware necessary to operate the system
How Does a Dipolar Bose-Einstein Condensate Collapse?
We emphasize that the macroscopic collapse of a dipolar Bose-Einstein
condensate in a pancake-shaped trap occurs through local density fluctuations,
rather than through a global collapse to the trap center. This hypothesis is
supported by a recent experiment in a chromium condensate.Comment: Proceedings of 17th International Laser Physics Worksho
One-dimensional Bose chemistry: effects of non-integrability
Three-body collisions of ultracold identical Bose atoms under tight
cylindrical confinement are analyzed. A Feshbach resonance in two-body
collisions is described by a two-channel zero-range interaction. Elimination of
the closed channel in the three-body problem reduces the interaction to a
one-channel zero-range one with an energy dependent strength. The related
problem with an energy independent strength (the Lieb-Liniger-McGuire model)
has an exact solution and forbids all chemical processes, such as three-atom
association and diatom dissociation, as well as reflection in atom-diatom
collisions. The resonant case is analyzed by a numerical solution of the
Faddeev-Lovelace equations. The results demonstrate that as the internal
symmetry of the Lieb-Liniger-McGuire model is lifted, the reflection and
chemical reactions become allowed and may be observed in experiments.Comment: 5 pages, 4 figure
Vortices and Ring Solitons in Bose-Einstein Condensates
The form and stability properties of axisymmetric and spherically symmetric
stationary states in two and three dimensions, respectively, are elucidated for
Bose-Einstein condensates. These states include the ground state, central
vortices, and radial excitations of both. The latter are called ring solitons
in two dimensions and spherical shells in three. The nonlinear Schrodinger
equation is taken as the fundamental model; both extended and harmonically
trapped condensates are considered. It is found that the presence of a vortex
stabilizes ring solitons in a harmonic trap, in contrast to the well known
instability of such solutions in the optics context. This is the first known
example of a dark soliton in the cubic nonlinear Schrodinger equation which is
stable in a number of dimensions greater than one.Comment: 15 pages, 9 figures -- final versio
Mixed perturbative expansion: the validity of a model for the cascading
A new type of perturbative expansion is built in order to give a rigorous
derivation and to clarify the range of validity of some commonly used model
equations.
This model describes the evolution of the modulation of two short and
localized pulses, fundamental and second harmonic, propagating together in a
bulk uniaxial crystal with non-vanishing second order susceptibility
and interacting through the nonlinear effect known as ``cascading'' in
nonlinear optics.
The perturbative method mixes a multi-scale expansion with a power series
expansion of the susceptibility, and must be carefully adapted to the physical
situation. It allows the determination of the physical conditions under which
the model is valid: the order of magnitude of the walk-off, phase-mismatch,and
anisotropy must have determined values.Comment: arxiv version is already officia
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