Vol 201, No 3 (2019)
- Year: 2019
- Articles: 11
- URL: https://journals.rcsi.science/0040-5779/issue/view/10523
Article
Andrei Alekseevich Slavnov
Spaces of Type S and Deformation Quantization
Abstract
We study the properties of the Gelfand-Shilov spaces \(S_{a_k}^{b_n}\) in the context of deformation quantization. Our main result is a characterization of their corresponding multiplier algebras with respect to a twisted convolution, which is given in terms of the inclusion relation between these algebras and the duals of the spaces of pointwise multipliers with an explicit description of these functional spaces. The proof of the inclusion theorem essentially uses the equality \(S_{a_k}^{b_n}=S^{b_n}\cap{S_{a_k}}\).
Matrix Extension of the Manakov-Santini System and an Integrable Chiral Model on an Einstein-Weyl Background
Abstract
We introduce an integrable matrix extension of the Manakov-Santini system and show that it describes a (2+1)-dimensional integrable chiral model in the Einstein-Weyl space. We apply a dressing scheme for the extended Manakov-Santini system and define an extended hierarchy. We also consider a matrix extension of a Toda-type system associated with another local form of the Einstein-Weyl geometry.
Physical Parameters of Solitary Wave Packets in Shallow Basins under Ice Cover
Abstract
We determine the velocities and lengths of solitary envelope waves whose velocity is located in a left half-neighborhood of the phase velocity minimum in the dispersion relation for shallow basins under ice cover. The ice cover is modeled as an elastic Kirchhoff-Love ice plate. The Euler equation for the liquid layer (water) includes an additional pressure from the plate, which Boats freely on the liquid surface. We consider the case of weakly nonlinear waves in the limit of long wavelengths and small amplitudes where the initial dimensionless stress in the ice cover does not exceed one third. These waves are described by a fifth-order Kawahara equation. We then compare the obtained results with the parameters found using a strongly nonlinear description. The comparison yields very good results for shallow depths of the considered basin. This phenomenon is explained by the properties of the lowest nonlinearity coefficient in the equations describing the solitary envelope waves branching from the phase velocity minimum on the dispersion curve. We discuss possible applications of the obtained results to experimental wave measurements under an ice cover.
Bilinearization and Soliton Solutions of a Supersymmetric Multicomponent Coupled Dispersionless Integrable System
Abstract
We present a supersymmetric generalization of a multicomponent coupled dispersionless (SUSY-MCD) integrable system. Expanding the superfields of the SUSY-MCD system, we obtain the component fermionic and bosonic held equations. We propose a bilinear form of the SUSY-MCD system and find soliton solutions of it.
Strongly Coupled B-Type Universal Characters and Hierarchies
Abstract
We construct a solution expressed in terms of Schur Q-functions of a strongly coupled B-type Kadomtsev-Petviashvili hierarchy. As a generalization of these functions, we introduce universal characters satisfying the bilinear equations of a new infinite-dimensional integrable system called the strongly coupled B-type universal character hierarchy.
Uniform Asymptotic Solution in the Form of an Airy Function for Semiclassical Bound States in One-Dimensional and Radially Symmetric Problems
Abstract
We consider stationary scalar and vector problems for differential and pseudodifferential operators leading to the appearance of asymptotic solutions of one-dimensional problems localized in a neighborhood of intervals (“bound states”). Based on the semiclassical approximation and the Maslov canonical operator, we develop a constructive algorithm that allows writing an asymptotic solution globally under certain conditions using an Airy function of complex argument.
Solutions of the Discrete Nonlinear Schrödinger Equation with a Trap
Abstract
We obtain solutions of the discrete nonlinear Schrödinger equation with an impurity center in two ways. In the first of them, we construct the wave function as a series in a certain parameter. In the second, approximate method, we obtain the wave function in the continuum limit. We compare the obtained solutions with numerical results, and the relative accuracy of the solution in the form of a series does not exceed 10−15in order of magnitude.
Wormholes in Jackiw—Teitelboim Gravity
Abstract
We investigate various aspects of AdS2 wormholes in Jackiw—Teitelboim gravity and their holographic applications. We first study the AdS2 space in global coordinates traversable by virtue of the presence of pointlike matter violating the dominant energy condition. We calculate the evolution of the entanglement entropy in such a system. We then investigate the construction proposed by Verlinde and colleagues describing states similar to wormholes. These states are called partially entangled thermal states. We propose a construction similar to the geometries of such states using conformal maps of the upper halfplane. We study correlation functions in theories dual to such geometries and also comment on the possible connection between a special type of partially entangled thermal states and violation of replica symmetry.
Gravitational Frequency Shift of Light Signals in a Pulsating Dark Matter Halo
Abstract
We study the gravitational frequency shift of light signals from the center of a spherically symmetric nonstatic matter distribution. In the case of oscillating scalar dark matter with a logarithmic potential, we obtain explicit formulas for the ratio of the emitted and received frequencies.
Bell Polynomials in the Mathematica System and Asymptotic Solutions of Integral Equations
Abstract
We consider the possibility of solving functional equations that arise when integrating homogeneous integral Fredholm equations of the second kind with a highly oscillatory kernel by using Bell polynomials. We review different types and properties of Bell polynomials. The focus of this paper is to promote using tools in the Bell polynomial package in the Mathematica system to solve certain problems in electrodynamics.