5,946 research outputs found
Negaton and Positon solutions of the soliton equation with self-consistent sources
The KdV equation with self-consistent sources (KdVES) is used as a model to
illustrate the method. A generalized binary Darboux transformation (GBDT) with
an arbitrary time-dependent function for the KdVES as well as the formula for
-times repeated GBDT are presented. This GBDT provides non-auto-B\"{a}cklund
transformation between two KdV equations with different degrees of sources and
enable us to construct more general solutions with arbitrary -dependent
functions. By taking the special -function, we obtain multisoliton,
multipositon, multinegaton, multisoliton-positon, multinegaton-positon and
multisoliton-negaton solutions of KdVES. Some properties of these solutions are
discussed.Comment: 13 pages, Latex, no figues, to be published in J. Phys. A: Math. Ge
The Solutions of the NLS Equations with Self-Consistent Sources
We construct the generalized Darboux transformation with arbitrary functions
in time for the AKNS equation with self-consistent sources (AKNSESCS)
which, in contrast with the Darboux transformation for the AKNS equation,
provides a non-auto-B\"{a}cklund transformation between two AKNSESCSs with
different degrees of sources. The formula for N-times repeated generalized
Darboux transformation is proposed. By reduction the generalized Darboux
transformation with arbitrary functions in time for the Nonlinear
Schr\"{o}dinger equation with self-consistent sources (NLSESCS) is obtained and
enables us to find the dark soliton, bright soliton and positon solutions for
NLSESCS and NLSESCS. The properties of these solution are analyzed.Comment: 24 pages, 3 figures, to appear in Journal of Physics A: Mathematical
and Genera
Effective spacetime from multi-dimensional gravity
We study the effective spacetimes in lower dimensions that can be extracted
from a multidimensional generalization of the Schwarzschild-Tangherlini
spacetimes derived by Fadeev, Ivashchuk and Melnikov ({\it Phys. Lett,} {\bf A
161} (1991) 98). The higher-dimensional spacetime has
dimensions, where and are the number of "internal" and "external" extra
dimensions, respectively. We analyze the effective spacetime obtained
after dimensional reduction of the external dimensions. We find that when
the extra dimensions are compact (i) the physics in lower dimensions is
independent of and the character of the singularities in higher dimensions,
and (ii) the total gravitational mass of the effective matter distribution
is less than the Schwarzshild mass. In contrast, when the extra dimensions
are large this is not so; the physics in does explicitly depend on
, as well as on the nature of the singularities in high dimensions, and the
mass of the effective matter distribution (with the exception of wormhole-like
distributions) is bigger than the Schwarzshild mass. These results may be
relevant to observations for an experimental/observational test of the theory.Comment: A typo in Eq. (24) is fixe
Generalized Darboux transformations for the KP equation with self-consistent sources
The KP equation with self-consistent sources (KPESCS) is treated in the
framework of the constrained KP equation. This offers a natural way to obtain
the Lax representation for the KPESCS. Based on the conjugate Lax pairs, we
construct the generalized binary Darboux transformation with arbitrary
functions in time for the KPESCS which, in contrast with the binary Darboux
transformation of the KP equation, provides a non-auto-B\"{a}cklund
transformation between two KPESCSs with different degrees. The formula for
N-times repeated generalized binary Darboux transformation is proposed and
enables us to find the N-soliton solution and lump solution as well as some
other solutions of the KPESCS.Comment: 20 pages, no figure
Propagating EUV disturbances in the solar corona : two-wavelength observations
Quasi-periodic EUV disturbances simultaneously observed in 171 Ã… and 195 Ã… TRACE bandpasses propagating outwardly in a fan-like magnetic structure of a coronal active region are analysed. Time series of disturbances observed in the different bandpasses have a relatively high correlation coefficient (up to about 0.7). The correlation has a tendency to decrease with distance along the structure: this is consistent with an interpretation of the disturbances in terms of parallel-propagating slow magnetoacoustic waves. The wavelet analysis does not show a significant difference between waves observed in different bandpasses. Periodic patterns of two distinct periods: 2-3 min and 5-8 min are detected in both bandpasses, existing simultaneously and at the same distance along the loop, suggesting the nonlinear generation of the second harmonics
Efficient fiber-optical interface for nanophotonic devices
We demonstrate a method for efficient coupling of guided light from a single
mode optical fiber to nanophotonic devices. Our approach makes use of
single-sided conical tapered optical fibers that are evanescently coupled over
the last ~10 um to a nanophotonic waveguide. By means of adiabatic mode
transfer using a properly chosen taper, single-mode fiber-waveguide coupling
efficiencies as high as 97(1)% are achieved. Efficient coupling is obtained for
a wide range of device geometries which are either singly-clamped on a chip or
attached to the fiber, demonstrating a promising approach for integrated
nanophotonic circuits, quantum optical and nanoscale sensing applications.Comment: 7 pages, 4 figures, includes supplementary informatio
Phase-Space analysis of Teleparallel Dark Energy
We perform a detailed dynamical analysis of the teleparallel dark energy
scenario, which is based on the teleparallel equivalent of General Relativity,
in which one adds a canonical scalar field, allowing also for a nonminimal
coupling with gravity. We find that the universe can result in the
quintessence-like, dark-energy-dominated solution, or to the stiff dark-energy
late-time attractor, similarly to standard quintessence. However, teleparallel
dark energy possesses an additional late-time solution, in which dark energy
behaves like a cosmological constant, independently of the specific values of
the model parameters. Finally, during the evolution the dark energy
equation-of-state parameter can be either above or below -1, offering a good
description for its observed dynamical behavior and its stabilization close to
the cosmological-constant value.Comment: 23 pages, 4 figures, 5 tables, version published at JCA
Ground state phases of the Half-Filled One-Dimensional Extended Hubbard Model
Using quantum Monte Carlo simulations, results of a strong-coupling
expansion, and Luttinger liquid theory, we determine quantitatively the ground
state phase diagram of the one-dimensional extended Hubbard model with on-site
and nearest-neighbor repulsions U and V. We show that spin frustration
stabilizes a bond-ordered (dimerized) state for U appr. V/2 up to U/t appr. 9,
where t is the nearest-neighbor hopping. The transition from the dimerized
state to the staggered charge-density-wave state for large V/U is continuous
for U up to appr. 5.5 and first-order for higher U.Comment: 4 pages, 4 figure
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