1,408 research outputs found
Boundary Conditions in Stepwise Sine-Gordon Equation and Multi-Soliton Solutions
We study the stepwise sine-Gordon equation, in which the system parameter is
different for positive and negative values of the scalar field. By applying
appropriate boundary conditions, we derive relations between the soliton
velocities before and after collisions. We investigate the possibility of
formation of heavy soliton pairs from light ones and vise versa. The concept of
soliton gun is introduced for the first time; a light pair is produced moving
with high velocity, after the annihilation of a bound, heavy pair. We also
apply boundary conditions to static, periodic and quasi-periodic solutions.Comment: 14 pages, 8 figure
Localized induction equation and pseudospherical surfaces
We describe a close connection between the localized induction equation
hierarchy of integrable evolution equations on space curves, and surfaces of
constant negative Gauss curvature.Comment: 21 pages, AMSTeX file. To appear in Journal of Physics A:
Mathematical and Genera
Dressing chain for the acoustic spectral problem
The iterations are studied of the Darboux transformation for the generalized
Schroedinger operator. The applications to the Dym and Camassa-Holm equations
are considered.Comment: 16 pages, 6 eps figure
B\"acklund Transformations of MKdV and Painlev\'e Equations
For there are and actions on the space of solutions of
the first nontrivial equation in the Z_2$ actions on the space of solutions of the standard MKdV equation.
These actions survive scaling reduction, and give rise to transformation groups
for certain (systems of) ODEs, including the second, fourth and fifth
Painlev\'e equations.Comment: 8 pages, plain te
Existence of superposition solutions for pulse propagation in nonlinear resonant media
Existence of self-similar, superposed pulse-train solutions of the nonlinear,
coupled Maxwell-Schr\"odinger equations, with the frequencies controlled by the
oscillator strengths of the transitions, is established. Some of these
excitations are specific to the resonant media, with energy levels in the
configurations of and and arise because of the interference
effects of cnoidal waves, as evidenced from some recently discovered identities
involving the Jacobian elliptic functions. Interestingly, these excitations
also admit a dual interpretation as single pulse-trains, with widely different
amplitudes, which can lead to substantially different field intensities and
population densities in different atomic levels.Comment: 11 Pages, 6 Figures, presentation changed and 3 figures adde
Proper time and Minkowski structure on causal graphs
For causal graphs we propose a definition of proper time which for small
scales is based on the concept of volume, while for large scales the usual
definition of length is applied. The scale where the change from "volume" to
"length" occurs is related to the size of a dynamical clock and defines a
natural cut-off for this type of clock. By changing the cut-off volume we may
probe the geometry of the causal graph on different scales and therey define a
continuum limit. This provides an alternative to the standard coarse graining
procedures. For regular causal lattice (like e.g. the 2-dim. light-cone
lattice) this concept can be proven to lead to a Minkowski structure. An
illustrative example of this approach is provided by the breather solutions of
the Sine-Gordon model on a 2-dimensional light-cone lattice.Comment: 15 pages, 4 figure
Interaction of Nonlinear Schr\"odinger Solitons with an External Potential
Employing a particularly suitable higher order symplectic integration
algorithm, we integrate the 1- nonlinear Schr\"odinger equation numerically
for solitons moving in external potentials. In particular, we study the
scattering off an interface separating two regions of constant potential. We
find that the soliton can break up into two solitons, eventually accompanied by
radiation of non-solitary waves. Reflection coefficients and inelasticities are
computed as functions of the height of the potential step and of its steepness.Comment: 14 pages, uuencoded PS-file including 10 figure
Bose-Einstein condensation in the presence of a uniform field and a point-like impurity
The behavior of an ideal -dimensional boson gas in the presence of a
uniform gravitational field is analyzed. It is explicitly shown that,
contrarily to an old standing folklore, the three-dimensional gas does not
undergo Bose-Einstein condensation at finite temperature. On the other hand,
Bose-Einstein condensation occurs at for if there is a
point-like impurity at the bottom of the vessel containing the gas.Comment: 14 pages, REVTEX. Revised version, accepted for publication in Phys.
Rev.
Discovery of New Ultracool White Dwarfs in the Sloan Digital Sky Survey
We report the discovery of five very cool white dwarfs in the Sloan Digital
Sky Survey (SDSS). Four are ultracool, exhibiting strong collision induced
absorption (CIA) from molecular hydrogen and are similar in color to the three
previously known coolest white dwarfs, SDSS J1337+00, LHS 3250 and LHS 1402.
The fifth, an ultracool white dwarf candidate, shows milder CIA flux
suppression and has a color and spectral shape similar to WD 0346+246. All five
new white dwarfs are faint (g > 18.9) and have significant proper motions. One
of the new ultracool white dwarfs, SDSS J0947, appears to be in a binary system
with a slightly warmer (T_{eff} ~ 5000K) white dwarf companion.Comment: 15 pages, 3 figures, submitted to ApJL. Higher resolution versions of
finding charts are available at
http://astro.uchicago.edu/~gates/findingchart
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