Soliton trains in Bose-Fermi mixtures

We theoretically consider the formation of bright solitons in a mixture of Bose and Fermi degenerate gases. While we assume the forces between atoms in a pure Bose component to be effectively repulsive, their character can be changed from repulsive to attractive in the presence of fermions provided the Bose and Fermi gases attract each other strongly enough. In such a regime the Bose component becomes a gas of effectively attractive atoms. Hence, generating bright solitons in the bosonic gas is possible. Indeed, after a sudden increase of the strength of attraction between bosons and fermions (realized by using a Feshbach resonance technique or by firm radial squeezing of both samples) soliton trains appear in the Bose-Fermi mixture.Comment: 4 pages, 4 figure

Quantum Many-Body Dynamics of Dark Solitons in Optical Lattices

We present a fully quantum many-body treatment of dark solitons formed by ultracold bosonic atoms in one-dimensional optical lattices. Using time-evolving block decimation to simulate the single-band Bose-Hubbard Hamiltonian, we consider the quantum dynamics of density and phase engineered dark solitons as well as the quantum evolution of mean-field dark solitons injected into the quantum model. The former approach directly models how one may create quantum entangled dark solitons in experiment. While we have already presented results regarding the latter approach elsewhere [Phys. Rev. Lett. {\bf 103}, 140403 (2009)], we expand upon those results in this work. In both cases, quantum fluctuations cause the dark soliton to fill in and may induce an inelasticity in soliton-soliton collisions. Comparisons are made to the Bogoliubov theory which predicts depletion into an anomalous mode that fills in the soliton. Our many-body treatment allows us to go beyond the Bogoliubov approximation and calculate explicitly the dynamics of the system's natural orbitals.Comment: 14 pages, 11 figures -- v3 has only minor changes from v2 -- this is the print versio

Stabilization of a light bullet in a layered Kerr medium with sign-changing nonlinearity

Using the numerical solution of the nonlinear Schr\"odinger equation and a variational method it is shown that (3+1)-dimensional spatiotemporal optical solitons, known as light bullets, can be stabilized in a layered Kerr medium with sign-changing nonlinearity along the propagation direction.Comment: 4 pages, 3 PS figure

The content of cytokines in the blood serum of patients with early latent syphilis in process of treatment.

Objective – to study the concentration of pro- and anti-inflammatory cytokines in patients with early latent syphilis before and after treatment. The study was conducted in 112 patients with early latent syphilis (52 men and 60 women) and 15 healthy persons of the control group – all aged 18-43. Serological tests were used: the classical complex of serological reactions (CSR), ELISA, the reaction of passive hemagglutination (RPGA), immunofluorescence reaction with absorption (RIF-abs) and RIF-200. Using ELISA, the levels of cytokines IL-2, IL-6, IL-10, TNFα, and INFγ were determined in serum (in patients with latent syphilis, before and after treatment). The analysis of the received data was carried out with application of the program package Statistics 6.0. To identify the relationships between the indices, Friedman's nonparametric variance analysis with the definition of χ2 was used. The concentration of IL-10 before treatment in patients with early latent syphilis was significantly increased by 3.7 (14.9±0.9 pg/ml compared to the control group 4.11±0.5 pg/ml). The dependence of the content of this cytokine on the period of infection was established. It was found that one year after treatment concentration of IL-10 remained 1.8 times higher. The concentration of IL-6 was increased by 6.5 times in patients with latent early syphilis and was also dependent on the period of the infection, and also even 1.5-2 years after treatment the IL-6 content remained elevated. It was also found that in patients with latent early syphilis the concentration of IL-2 was increased by 2.3 times and it did not normalize in 24.5% of patients even two years after treatment. In patients with latent early syphilis, the concentration of TNFα was increased by 3.6 times. After treatment, the concentration of TNFα decreased, but exceeded the control values by 1.55 times. Further analysis of the concentration of TNFα revealed that, with a disease period of up to one year, the concentration of this cytokine was normal during ten months after treatment, and in patients with the disease period of more than one year, after treatment normalization of the TNFα level was absent in 64.5% even after 18 months. It was found that the concentration of INFγ in patients with early latent syphilis before treatment was increased by 3.8 times in comparison with the control group. After treatment, almost 25 % of patients with the duration of the infection more than one year revealed no normalization of INFγ and it was increased by 1.5 times. In patients with latent early syphilis there was a significant increase in the concentration of cytokines TNFα and INFγ, an imbalance of IL-2, IL-6, IL-10 as well as. The dependence of the cytokine concentration on the period of infection is noted. Based on the study of the cytokine status in patients with early latent syphilis with periods of infection of more than one year, the use of immunomodulatory therapy may be recommended. Increasing the concentration of such cytokines as TNFα, IL-6, IL-10 after treatment can be used as prognostic tests of serological resistance

Combination of inverse spectral transform method and method of characteristics: deformed Pohlmeyer equation

We apply a version of the dressing method to a system of four dimensional nonlinear Partial Differential Equations (PDEs), which contains both Pohlmeyer equation (i.e. nonlinear PDE integrable by the Inverse Spectral Transform Method) and nonlinear matrix PDE integrable by the method of characteristics as particular reductions. Some other reductions are suggested.Comment: 12 page

Modulated wavepackets associated with longitudinal dust grain oscillations in a dusty plasma crystal

The nonlinear amplitude modulation of longitudinal dust lattice waves (LDLWs) propagating in a dusty plasma crystal is investigated in a continuum approximation. It is shown that long wavelength LDLWs are modulationally stable, while shorter wavelengths may be unstable. The possibility for the formation and propagation of different envelope localized excitations is discussed. It is shown that the total grain displacement bears a (weak) constant displacement (zeroth harmonic mode), due to the asymmetric form of the nonlinear interaction potential. The existence of asymmetric envelope localized modes is predicted. The types and characteristics of these coherent nonlinear structures are discussed.Comment: 18 pages, 7 figures, to appear in Physics of Plasma

Integrated Lax Formalism for PCM

By solving the first-order algebraic field equations which arise in the dual formulation of the D=2 principal chiral model (PCM) we construct an integrated Lax formalism built explicitly on the dual fields of the model rather than the currents. The Lagrangian of the dual scalar field theory is also constructed. Furthermore we present the first-order PDE system for an exponential parametrization of the solutions and discuss the Frobenious integrability of this system.Comment: 24 page

Stabilization of a (3+1)D soliton in a Kerr medium by a rapidly oscillating dispersion coefficient

Using the numerical solution of the nonlinear Schroedinger equation and a variational method it is shown that (3+1)-dimensional spatiotemporal optical solitons can be stabilized by a rapidly oscillating dispersion coefficient in a Kerr medium with cubic nonlinearity. This has immediate consequence in generating dispersion-managed robust optical soliton in communication as well as possible stabilized Bose-Einstein condensates in periodic optical-lattice potential via an effective-mass formulation. We also critically compare the present stabilization with that obtained by a rapid sinusoidal oscillation of the Kerr nonlinearity parameter.Comment: 6 pages, 6 ps figures, New figure 4 added, Physical Review

Stabilization of bright solitons and vortex solitons in a trapless three-dimensional Bose-Einstein condensate by temporal modulation of the scattering length

Using variational and numerical solutions of the mean-field Gross-Pitaevskii equation we show that a bright soliton can be stabilized in a trapless three-dimensional attractive Bose-Einstein condensate (BEC) by a rapid periodic temporal modulation of scattering length alone by using a Feshbach resonance. This scheme also stabilizes a rotating vortex soliton in two dimensions. Apart from possible experimental application in BEC, the present study suggests that the spatiotemporal solitons of nonlinear optics in three dimensions can also be stabilized in a layered Kerr medium with sign-changing nonlinearity along the propagation direction.Comment: 6 pages, 7 PS figure