Observation of Linear and Nonlinear Light Localization at the Edges of Moiré Arrays.

We observe linear and nonlinear light localization at the edges and in the corners of truncated moiré arrays created by the superposition of periodic mutually twisted at Pythagorean angles square sublattices. Experimentally exciting corner linear modes in the femtosecond-laser written moiré arrays we find drastic differences in their localization properties in comparison with the bulk excitations. We also address the impact of nonlinearity on the corner and bulk modes and experimentally observe the crossover from linear quasilocalized states to the surface solitons emerging at the higher input powers. Our results constitute the first experimental demonstration of localization phenomena induced by truncation of periodic moiré structures in photonic systems.

Motion of dark solitons in a non-uniform flow of Bose-Einstein condensate.

We study motion of dark solitons in a non-uniform one-dimensional flow of a Bose-Einstein condensate. Our approach is based on Hamiltonian mechanics applied to the particle-like behavior of dark solitons in a slightly non-uniform and slowly changing surrounding. In one-dimensional geometry, the condensate's wave function undergoes the jump-like behavior across the soliton, and this leads to generation of the counterflow in the background condensate. For a correct description of soliton's dynamics, the contributions of this counterflow to the momentum and energy of the soliton are taken into account. The resulting Hamilton equations are reduced to the Newton-like equation for the soliton's path, and this Newton equation is solved in several typical situations. The analytical results are confirmed by numerical calculations.

Bragg solitons in topological Floquet insulators.

We consider a topological Floquet insulator consisting of two honeycomb arrays of identical waveguides having opposite helicities. The interface between the arrays supports two distinct topological edge states, which can be resonantly coupled by additional weak longitudinal refractive index modulation with a period larger than the helix period. In the presence of Kerr nonlinearity, such coupled edge states enable topological Bragg solitons. Theory and examples of such solitons are presented.

Simple waves in a two-component Bose-Einstein condensate.

We study the dynamics of so-called simple waves in a two-component Bose-Einstein condensate. The evolution of the condensate is described by Gross-Pitaevskii equations which can be reduced for these simple wave solutions to a system of ordinary differential equations which coincide with those derived by Ovsyannikov for the two-layer fluid dynamics. We solve the Ovsyannikov system for two typical situations of large and small difference between interspecies and intraspecies nonlinear interaction constants. Our analytic results are confirmed by numerical simulations.

Evolution of initial discontinuities in the Riemann problem for the Kaup-Boussinesq equation with positive dispersion.

We consider the space-time evolution of initial discontinuities of depth and flow velocity for an integrable version of the shallow water Boussinesq system introduced by Kaup. We focus on a specific version of this "Kaup-Boussinesq model" for which a flat water surface is modulationally stable, we speak below of "positive dispersion" model. This model also appears as an approximation to the equations governing the dynamics of polarisation waves in two-component Bose-Einstein condensates. We describe its periodic solutions and the corresponding Whitham modulation equations. The self-similar, one-phase wave structures are composed of different building blocks, which are studied in detail. This makes it possible to establish a classification of all the possible wave configurations evolving from initial discontinuities. The analytic results are confirmed by numerical simulations.

Solution of the Riemann problem for polarization waves in a two-component Bose-Einstein condensate.

We provide a classification of the possible flows of two-component Bose-Einstein condensates evolving from initially discontinuous profiles. We consider the situation where the dynamics can be reduced to the consideration of a single polarization mode (also denoted as "magnetic excitation") obeying a system of equations equivalent to the Landau-Lifshitz equation for an easy-plane ferromagnet. We present the full set of one-phase periodic solutions. The corresponding Whitham modulation equations are obtained together with formulas connecting their solutions with the Riemann invariants of the modulation equations. The problem is not genuinely nonlinear, and this results in a non-single-valued mapping of the solutions of the Whitham equations with physical wave patterns as well as the appearance of interesting elements-contact dispersive shock waves-that are absent in more standard, genuinely nonlinear situations. Our analytic results are confirmed by numerical simulations.

[Comparative study of sialyltransferases in cultured cells of the rat embryo, transformed by DNA bovine adenovirus type 3]. / Sravnitel'noe izuchenie sialiltransferaz v kul'turakh kletok émbrionov krys, transformirovannykh DNK bych'ego adenovirusa tipa 3.

The specific activities of membrane-bound sialyl transferases from six cultures of cells transformed by bovine adenovirus DNA type 3 (BA-3) before and after passage through host animal organism were compared. The sialyl transferase activity was increased with respect to the high molecular weight acceptor, asialylofetuin in the majority of transformed and tumour cultures. Identification of sialylation products by paper chromatography revealed that all cell cultures contain sialyltransferases synthesizing neuraminosyl-alpha (2----6)N-acetyllactosamine. The pH dependence of activities of the membrane-bound enzymes were studied. An additional pH optimum (5.5-6.0) of endogenous activity was revealed in most of transformed cultures. Using isoelectrofocusing of detergent extracts in sucrose density gradient, the presence of multiple forms of the enzyme was revealed in all cultures under study. In most virulent strains, Op2a/4 and OAB2a, the forms possessing a high exogenous activity at pH gradient 6.0-6.5 were activated. The multiple forms of line Op2a/4 were investigated at pH 5.8-6.3 and 7.6-8.0. It was shown that the forms with different pI have different pH optima. A correlation between the changes in the activities of sialyl transferases and the increase of oncogenicity of transformed cells after their passage through host organism was detected only in one group of transformed cells.