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 $\alpha_3$ ($\alpha_3$ is the coefficient in the third derivative term) and vanish at $\alpha_3 \to 0$. The most essential, at small $\alpha_3$, 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 $f(x,t) = a \exp[i K(t) x]$, 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 $f(x)$. 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 $f(x)$. In order to find out for which regions the above solutions are stable, we calculate the time evolution of the soliton momentum $P(t)$ and soliton velocity $V(t)$: This is a parameter representation of a curve $P(V)$ 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 $\kappa$ which characterizes the soliton amplitude exhibits loglognormal divergence near the maximum possible $\kappa$ value.Comment: 8 pages, 4 figure