Reflection of Channel-Guided Solitons at Junctions in Two-Dimensional Nonlinear Schroedinger Equation

Solitons confined in channels are studied in the two-dimensional nonlinear Schr\"odinger equation. We study the dynamics of two channel-guided solitons near the junction where two channels are merged. The two solitons merge into one soliton, when there is no phase shift. If a phase difference is given to the two solitons, the Josephson oscillation is induced. The Josephson oscillation is amplified near the junction. The two solitons are reflected when the initial velocity is below a critical value.Comment: 3 pages, 2 figure

Notes on Five-dimensional Kerr Black Holes

The geometry of five-dimensional Kerr black holes is discussed based on geodesics and Weyl curvatures. Kerr-Star space, Star-Kerr space and Kruskal space are naturally introduced by using special null geodesics. We show that the geodesics of AdS Kerr black hole are integrable, which generalizes the result of Frolov and Stojkovic. We also show that five-dimensional AdS Kerr black holes are isospectrum deformations of Ricci-flat Kerr black holes in the sense that the eigenvalues of the Weyl curvature are preserved.Comment: 23 pages, 5 figures; analyses on the Weyl curvature of AdS Kerr black holes are extended, an appendix and references are adde

Higher-order vortex solitons, multipoles, and supervortices on a square optical lattice

We predict new generic types of vorticity-carrying soliton complexes in a class of physical systems including an attractive Bose-Einstein condensate in a square optical lattice (OL) and photonic lattices in photorefractive media. The patterns include ring-shaped higher-order vortex solitons and supervortices. Stability diagrams for these patterns, based on direct simulations, are presented. The vortex ring solitons are stable if the phase difference \Delta \phi between adjacent solitons in the ring is larger than \pi/2, while the supervortices are stable in the opposite case, \Delta \phi <\pi /2. A qualitative explanation to the stability is given.Comment: 9 pages, 4 figure

Gap solitons in Bragg gratings with a harmonic superlattice

Solitons are studied in a model of a fiber Bragg grating (BG) whose local reflectivity is subjected to periodic modulation. The superlattice opens an infinite number of new bandgaps in the model's spectrum. Averaging and numerical continuation methods show that each gap gives rise to gap solitons (GSs), including asymmetric and double-humped ones, which are not present without the superlattice.Computation of stability eigenvalues and direct simulation reveal the existence of completely stable families of fundamental GSs filling the new gaps - also at negative frequencies, where the ordinary GSs are unstable. Moving stable GSs with positive and negative effective mass are found too.Comment: 7 pages, 3 figures, submitted to EP

Multiple treg suppressive modules and their adaptability

Foxp3+ regulatory T cells (Tregs) are a constitutively immunosuppressive cell type critical for the control of autoimmunity and inflammatory pathology. A range of mechanisms of Treg suppression have been identified and it has not always been clear how these different mechanisms interact in order to properly suppress autoimmunity and excessive inflammation. In recent years it has become clear that, while all Tregs seem to share some core suppressive mechanisms, they are also able to adapt to their surroundings in response to a variety of stimuli by homing to the sites of inflammation and exerting ancillary suppressive functions. In this review, we discuss the relevance and possible modes of Treg adaptability and put forward a modular model of Treg suppressive function. Understanding this flexibility may hold the key to understanding the full spectrum of Treg suppressive behavior

Nonlinear management of topological solitons in a spin-orbit-coupled system

We consider possibilities to control dynamics of solitons of two types, maintained by the combination of cubic attraction and spin-orbit coupling (SOC) in a two-component system, namely, semi-dipoles (SDs) and mixed modes (MMs), by making the relative strength of the cross-attraction, gamma, a function of time periodically oscillating around the critical value, gamma = 1, which is an SD/MM stability boundary in the static system. The structure of SDs is represented by the combination of a fundamental soliton in one component and localized dipole mode in the other, while MMs combine fundamental and dipole terms in each component. Systematic numerical analysis reveals a finite bistability region for the SDs and MMs around gamma = 1, which does not exist in the absence of the periodic temporal modulation ("management"), as well as emergence of specific instability troughs and stability tongues for the solitons of both types, which may be explained as manifestations of resonances between the time-periodic modulation and intrinsic modes of the solitons. The system can be implemented in Bose-Einstein condensates, and emulated in nonlinear optical waveguides.Comment: to be published in Symmetry (special issue "Non-linear Topological Photonics"

Stochastic synchronization in globally coupled phase oscillators

Cooperative effects of periodic force and noise in globally Cooperative effects of periodic force and noise in globally coupled systems are studied using a nonlinear diffusion equation for the number density. The amplitude of the order parameter oscillation is enhanced in an intermediate range of noise strength for a globally coupled bistable system, and the order parameter oscillation is entrained to the external periodic force in an intermediate range of noise strength. These enhancement phenomena of the response of the order parameter in the deterministic equations are interpreted as stochastic resonance and stochastic synchronization in globally coupled systems.Comment: 5 figure

Gap solitons in quasiperiodic optical lattices

Families of solitons in one- and two-dimensional (1D and 2D) Gross-Pitaevskii equations with the repulsive nonlinearity and a potential of the quasicrystallic type are constructed (in the 2D case, the potential corresponds to a five-fold optical lattice). Stable 1D solitons in the weak potential are explicitly found in three bandgaps. These solitons are mobile, and they collide elastically. Many species of tightly bound 1D solitons are found in the strong potential, both stable and unstable (unstable ones transform themselves into asymmetric breathers). In the 2D model, families of both fundamental and vortical solitons are found and are shown to be stable.Comment: 8 pages, 11 figure

Quantum switches and quantum memories for matter-wave lattice solitons

We study the possibility of implementing a quantum switch and a quantum memory for matter wave lattice solitons by making them interact with "effective" potentials (barrier/well) corresponding to defects of the optical lattice. In the case of interaction with an "effective" potential barrier, the bright lattice soliton experiences an abrupt transition from complete transmission to complete reflection (quantum switch) for a critical height of the barrier. The trapping of the soliton in an "effective" potential well and its release on demand, without loses, shows the feasibility of using the system as a quantum memory. The inclusion of defects as a way of controlling the interactions between two solitons is also reported

Resonant nonlinearity management for nonlinear-Schr\"{o}dinger solitons

We consider effects of a periodic modulation of the nonlinearity coefficient on fundamental and higher-order solitons in the one-dimensional NLS equation, which is an issue of direct interest to Bose-Einstein condensates in the context of the Feshbach-resonance control, and fiber-optic telecommunications as concerns periodic compensation of the nonlinearity. We find from simulations, and explain by means of a straightforward analysis, that the response of a fundamental soliton to the weak perturbation is resonant, if the modulation frequency $\omega$ is close to the intrinsic frequency of the soliton. For higher-order $n$-solitons with $n=2$ and 3, the response to an extremely weak perturbation is also resonant, if $\omega$ is close to the corresponding intrinsic frequency. More importantly, a slightly stronger drive splits the 2- or 3-soliton, respectively, into a set of two or three moving fundamental solitons. The dependence of the threshold perturbation amplitude, necessary for the splitting, on $\omega$ has a resonant character too. Amplitudes and velocities of the emerging fundamental solitons are accurately predicted, using exact and approximate conservation laws of the perturbed NLS equation.Comment: 14 pages, 6 figure