602 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
Teaching Note—Teaching Trumpism
The election of Donald Trump was an astounding moment in the history of the United States. As academics across disciplines and social work as a profession struggled to understand the election and its effects, several syllabi were crowd sourced to explain the phenomenon known as Trumpism. This article describes a social work social policy course derived from these syllabi, as well as the pedagogical choices and consequences of teaching this course at the graduate level
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
Spatial Solitons in Media with Delayed-Response Optical Nonlinearities
Near-soliton scanning light-beam propagation in media with both
delayed-response Kerr-type and thermal nonlinearities is analyzed. The
delayed-response part of the Kerr nonlinearity is shown to be competitive as
compared to the thermal nonlinearity, and relevant contributions to a
distortion of the soliton form and phase can be mutually compensated. This
quasi-soliton beam propagation regime keeps properties of the incli- ned
self-trapped channel.Comment: 7 pages, to be published in Europhys. Let
Instability and Evolution of Nonlinearly Interacting Water Waves
We consider the modulational instability of nonlinearly interacting
two-dimensional waves in deep water, which are described by a pair of
two-dimensional coupled nonlinear Schroedinger equations. We derive a nonlinear
dispersion relation. The latter is numerically analyzed to obtain the regions
and the associated growth rates of the modulational instability. Furthermore,
we follow the long term evolution of the latter by means of computer
simulations of the governing nonlinear equations and demonstrate the formation
of localized coherent wave envelopes. Our results should be useful for
understanding the formation and nonlinear propagation characteristics of large
amplitude freak waves in deep water.Comment: 4 pages, 4 figures, to appear in Physical Review Letter
New features of modulational instability of partially coherent light; importance of the incoherence spectrum
It is shown that the properties of the modulational instability of partially
coherent waves propagating in a nonlinear Kerr medium depend crucially on the
profile of the incoherent field spectrum. Under certain conditions, the
incoherence may even enhance, rather than suppress, the instability. In
particular, it is found that the range of modulationally unstable wave numbers
does not necessarily decrease monotonously with increasing degree of
incoherence and that the modulational instability may still exist even when
long wavelength perturbations are stable.Comment: 4 pages, 2 figures, submitted to Phys. Rev. Let
Shock waves in the dissipative Toda lattice
We consider the propagation of a shock wave (SW) in the damped Toda lattice.
The SW is a moving boundary between two semi-infinite lattice domains with
different densities. A steadily moving SW may exist if the damping in the
lattice is represented by an ``inner'' friction, which is a discrete analog of
the second viscosity in hydrodynamics. The problem can be considered
analytically in the continuum approximation, and the analysis produces an
explicit relation between the SW's velocity and the densities of the two
phases. Numerical simulations of the lattice equations of motion demonstrate
that a stable SW establishes if the initial velocity is directed towards the
less dense phase; in the opposite case, the wave gradually spreads out. The
numerically found equilibrium velocity of the SW turns out to be in a very good
agreement with the analytical formula even in a strongly discrete case. If the
initial velocity is essentially different from the one determined by the
densities (but has the correct sign), the velocity does not significantly
alter, but instead the SW adjusts itself to the given velocity by sending
another SW in the opposite direction.Comment: 10 pages in LaTeX, 5 figures available upon regues
Variational approximation and the use of collective coordinates
We consider propagating, spatially localized waves in a class of equations that contain variational and nonvariational terms. The dynamics of the waves is analyzed through a collective coordinate approach. Motivated by the variational approximation, we show that there is a natural choice of projection onto collective variables for reducing the governing (nonlinear) partial differential equation (PDE) to coupled ordinary differential equations (ODEs). This projection produces ODEs whose solutions are exactly the stationary states of the effective Lagrangian that would be considered in applying the variational approximation method. We illustrate our approach by applying it to a modified Fisher equation for a traveling front, containing a non-constant-coefficient nonlinear term. We present numerical results that show that our proposed projection captures both the equilibria and the dynamics of the PDE much more closely than previously proposed projections. © 2013 American Physical Society
Solitary Waves Under the Competition of Linear and Nonlinear Periodic Potentials
In this paper, we study the competition of linear and nonlinear lattices and
its effects on the stability and dynamics of bright solitary waves. We consider
both lattices in a perturbative framework, whereby the technique of Hamiltonian
perturbation theory can be used to obtain information about the existence of
solutions, and the same approach, as well as eigenvalue count considerations,
can be used to obtained detailed conditions about their linear stability. We
find that the analytical results are in very good agreement with our numerical
findings and can also be used to predict features of the dynamical evolution of
such solutions.Comment: 13 pages, 4 figure
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