716 research outputs found
Dynamics of Solitons and Quasisolitons of Cubic Third-Order Nonlinear Schr\"odinger Equation
The dynamics of soliton and quasisoliton solutions of cubic third order
nonlinear Schr\"{o}dinger equation is studied. The regular solitons exist due
to a balance between the nonlinear terms and (linear) third order dispersion;
they are not important at small ( is the coefficient in
the third derivative term) and vanish at . The most essential,
at small , is a quasisoliton emitting resonant radiation (resonantly
radiating soliton). Its relationship with the other (steady) quasisoliton,
called embedded soliton, is studied analytically and in numerical experiments.
It is demonstrated that the resonantly radiating solitons emerge in the course
of nonlinear evolution, which shows their physical significance
Perturbation theory for localized solutions of sine-Gordon equation: decay of a breather and pinning by microresistor
We develop a perturbation theory that describes bound states of solitons
localized in a confined area. External forces and influence of inhomogeneities
are taken into account as perturbations to exact solutions of the sine-Gordon
equation. We have investigated two special cases of fluxon trapped by a
microresistor and decay of a breather under dissipation. Also, we have carried
out numerical simulations with dissipative sine-Gordon equation and made
comparison with the McLaughlin-Scott theory. Significant distinction between
the McLaughlin-Scott calculation for a breather decay and our numerical result
indicates that the history dependence of the breather evolution can not be
neglected even for small damping parameter
Dynamics of shallow dark solitons in a trapped gas of impenetrable bosons
The dynamics of linear and nonlinear excitations in a Bose gas in the
Tonks-Girardeau (TG) regime with longitudinal confinement are studied within a
mean field theory of quintic nonlinearity. A reductive perturbation method is
used to demonstrate that the dynamics of shallow dark solitons, in the presence
of an external potential, can effectively be described by a
variable-coefficient Korteweg-de Vries equation. The soliton oscillation
frequency is analytically obtained to be equal to the axial trap frequency, in
agreement with numerical predictions obtained by Busch {\it et al.} [J. Phys. B
{\bf 36}, 2553 (2003)] via the Bose-Fermi mapping. We obtain analytical
expressions for the evolution of both soliton and emitted radiation (sound)
profiles.Comment: 4 pages, Phys. Rev. A (in press
Magnetosonic solitons in a dusty plasma slab
The existence of magnetosonic solitons in dusty plasmas is investigated. The
nonlinear magnetohydrodynamic equations for a warm dusty magnetoplasma are thus
derived. A solution of the nonlinear equations is presented. It is shown that,
due to the presence of dust, static structures are allowed. This is in sharp
contrast to the formation of the so called shocklets in usual magnetoplasmas. A
comparatively small number of dust particles can thus drastically alter the
behavior of the nonlinear structures in magnetized plasmas.Comment: 7 pages, 6 figure
Scattering and Trapping of Nonlinear Schroedinger Solitons in External Potentials
Soliton motion in some external potentials is studied using the nonlinear
Schr\"odinger equation. Solitons are scattered by a potential wall. Solitons
propagate almost freely or are trapped in a periodic potential. The critical
kinetic energy for reflection and trapping is evaluated approximately with a
variational method.Comment: 9 pages, 7 figure
Can One Distinguish Tau Neutrinos from Antineutrinos in Neutral-Current Pion Production Processes?
A potential way to distinguish tau-neutrinos from antineutrinos, below the
tau-production threshold, but above the pion production one, is presented. It
is based on the different behavior of the neutral current pion production off
the nucleon, depending on whether it is induced by neutrinos or antineutrinos.
This procedure for distinguishing tau-neutrinos from antineutrinos neither
relies on any nuclear model, nor it is affected by any nuclear effect
(distortion of the outgoing nucleon waves, etc...). We show that
neutrino-antineutrino asymmetries occur both in the totally integrated cross
sections and in the pion azimuthal differential distributions. To define the
asymmetries for the latter distributions we just rely on Lorentz-invariance.
All these asymmetries are independent of the lepton family and can be
experimentally measured by using electron or muon neutrinos, due to the lepton
family universality of the neutral current neutrino interaction. Nevertheless
and to estimate their size, we have also used the chiral model of
hep-ph/0701149 at intermediate energies. Results are really significant since
the differences between neutrino and antineutrino induced reactions are always
large in all physical channels.Comment: Revised version. 8 pages, 3 figures. The abstract has been changed
and discussion extende
Solitons in cavity-QED arrays containing interacting qubits
We reveal the existence of polariton soliton solutions in the array of weakly
coupled optical cavities, each containing an ensemble of interacting qubits. An
effective complex Ginzburg-Landau equation is derived in the continuum limit
taking into account the effects of cavity field dissipation and qubit
dephasing. We have shown that an enhancement of the induced nonlinearity can be
achieved by two order of the magnitude with a negative interaction strength
which implies a large negative qubit-field detuning as well. Bright solitons
are found to be supported under perturbations only in the upper (optical)
branch of polaritons, for which the corresponding group velocity is controlled
by tuning the interacting strength. With the help of perturbation theory for
solitons, we also demonstrate that the group velocity of these polariton
solitons is suppressed by the diffusion process
Four in Ten Adults with Disabilities Experienced Unfair Treatment in Health Care Settings, at Work, or When Applying for Public Benefits in 2022
In this brief, we used December 2022 data from a nationally representative survey of adults ages 18 to 64 to examine rates at which adults with and without disabilities reported they were treated or judged unfairly in the past year in three settings: at doctors' offices, clinics, or hospitals; at work; and when applying for public benefits. We also examined the impact of such treatment on their well-being.Despite important federal antidiscrimination protections, people with disabilities experience unfair treatment in health care settings, workplaces, and when applying for public benefits. Understanding and addressing these experiences is necessary to ensure that people with disabilities have equitable access to health care, employment opportunities, and economic support essential for meeting basic needs
Nonlinear Schr\"odinger Equation with Spatio-Temporal Perturbations
We investigate the dynamics of solitons of the cubic Nonlinear Schr\"odinger
Equation (NLSE) with the following perturbations: non-parametric
spatio-temporal driving of the form , damping, and a
linear term which serves to stabilize the driven soliton. Using the time
evolution of norm, momentum and energy, or, alternatively, a Lagrangian
approach, we develop a Collective-Coordinate-Theory which yields a set of ODEs
for our four collective coordinates. These ODEs are solved analytically and
numerically for the case of a constant, spatially periodic force . The
soliton position exhibits oscillations around a mean trajectory with constant
velocity. This means that the soliton performs, on the average, a
unidirectional motion although the spatial average of the force vanishes. The
amplitude of the oscillations is much smaller than the period of . In
order to find out for which regions the above solutions are stable, we
calculate the time evolution of the soliton momentum and soliton
velocity : This is a parameter representation of a curve which is
visited by the soliton while time evolves. Our conjecture is that the soliton
becomes unstable, if this curve has a branch with negative slope. This
conjecture is fully confirmed by our simulations for the perturbed NLSE.
Moreover, this curve also yields a good estimate for the soliton lifetime: the
soliton lives longer, the shorter the branch with negative slope is.Comment: 21 figure
Numerical study on diverging probability density function of flat-top solitons in an extended Korteweg-de Vries equation
We consider an extended Korteweg-de Vries (eKdV) equation, the usual
Korteweg-de Vries equation with inclusion of an additional cubic nonlinearity.
We investigate the statistical behaviour of flat-top solitary waves described
by an eKdV equation in the presence of weak dissipative disorder in the linear
growth/damping term. With the weak disorder in the system, the amplitude of
solitary wave randomly fluctuates during evolution. We demonstrate numerically
that the probability density function of a solitary wave parameter
which characterizes the soliton amplitude exhibits loglognormal divergence near
the maximum possible value.Comment: 8 pages, 4 figure
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