On the internal modes in sine-Gordon chain

We address the issue of internal modes of a kink of a discrete sine-Gordon equation. The main point of the present study is to elucidate how the antisymmetric internal mode frequency dependence enters the quasicontinuum spectrum of nonlocalized waves. We analyze the internal frequency dependencies as functions of both the number of cites and discreteness parameter and explain the origin of spectrum peculiarity which arises after the frequency dependence of antisymmetric mode returns back to the continuous spectrum at some nonzero value of the intersite coupling.Comment: 5 pages, 3 figure

Scattering of vortex pairs in 2D easy-plane ferromagnets

Vortex-antivortex pairs in 2D easy-plane ferromagnets have characteristics of solitons in two dimensions. We investigate numerically and analytically the dynamics of such vortex pairs. In particular we simulate numerically the head-on collision of two pairs with different velocities for a wide range of the total linear momentum of the system. If the momentum difference of the two pairs is small, the vortices exchange partners, scatter at an angle depending on this difference, and form two new identical pairs. If it is large, the pairs pass through each other without losing their identity. We also study head-tail collisions. Two identical pairs moving in the same direction are bound into a moving quadrupole in which the two vortices as well as the two antivortices rotate around each other. We study the scattering processes also analytically in the frame of a collective variable theory, where the equations of motion for a system of four vortices constitute an integrable system. The features of the different collision scenarios are fully reproduced by the theory. We finally compare some aspects of the present soliton scattering with the corresponding situation in one dimension.Comment: 13 pages (RevTeX), 8 figure

Group analysis and renormgroup symmetries

An original regular approach to constructing special type symmetries for boundary value problems, namely renormgroup symmetries, is presented. Different methods of calculating these symmetries, based on modern group analysis are described. Application of the approach to boundary value problems is demonstrated with the help of a simple mathematical model.Comment: 17 pages, RevTeX LATeX file, to appear in Journal of Mathematical Physic

VLBI detection of the HST-1 feature in the M87 jet at 2 cm

A bright feature 80 pc away from the core in the powerful jet of M87 shows highly unusual properties. Earlier radio, optical and X-ray observations have shown that this feature, labeled HST-1, is superluminal, and is possibly connected with the TeV flare detected by HESS in 2005. It has been claimed that this feature might have a blazar nature, due to these properties. To examine the possible blazar-like nature of HST-1, we analyzed lambda 2 cm VLBA archival data from dedicated full-track observations and the 2 cm survey/MOJAVE VLBI monitoring programs obtained between 2000 and 2009. Applying VLBI wide-field imaging techniques, the HST-1 region was imaged at milliarcsecond resolution. Here we present the first 2 cm VLBI detection of this feature in observations from early 2003 to early 2007, and analyze its evolution over this time. Using the detections of HST-1, we find that the projected apparent speed is 0.61 +/- 0.31 c. A comparison of the VLA and VLBA flux densities of this feature indicate that is mostly resolved on molliarcsecond scales. This feature is optically thin between lambda 2 cm and lambda 20 cm. We do not find evidence of a blazar nature for HST-1.Comment: 9 pages, 9 figures, accepted by Astronomy and Astrophysic

Aharonov-Casher effect in a two dimensional hole gas with spin-orbit interaction

We study the quantum interference effects induced by the Aharonov-Casher phase in a ring structure in a two-dimensional heavy hole (HH) system with spin-orbit interaction realizable in narrow asymmetric quantum wells. The influence of the spin-orbit interaction strength on the transport is investigated analytically. These analytical results allow us to explain the interference effects as a signature of the Aharonov-Casher Berry phases. Unlike previous studies on the electron two-dimensional Rashba systems, we find that the frequency of conductance modulations as a function of the spin-orbit strength is not constant but increases for larger spin-orbit splittings. In the limit of thin channel rings (width smaller than Fermi wavelength), we find that the spin-orbit splitting can be greatly increased due to quantization in the radial direction. We also study the influence of magnetic field considering both limits of small and large Zeeman splittings.Comment: 6 pages, 4 figure