Russian Journal of Mathematical Physics最新文献

This paper is devoted to the mathematical part of the inverse problem of reconstructing the magnetic structure in AGN jets from data on the rotation measure for the polarization angle of synchrotron emission from relativistic electrons. Based on the azimuthal symmetry of the helical field, we show how the reconstruction problem reduces to the integral Abel equation. By giving a solution to this equation, we formulate the constraints on the magnetic field components and thermal electron density under which the problem has a unique and stable solution. These results may be useful to astrophysicists and experts in integral equations and inverse problems.

A nonlinear singularly perturbed second-order ordinary differential equation (ODE) is considered, in which one of the nonlinear arguments is nonlocal and depends on the control parameter. An asymptotic solution to the Neumann problem with an interior transition layer is constructed. The location of the transition point depends on the value of the control parameter. The effect of stabilization of the nonlocal argument with respect to the control parameter is that, as the control parameter changes over a certain range of values, the nonlocal argument changes asymptotically little. The existence of a solution with the asymptotic behavior of this type is proven, and examples of applying the general theory to specific models are considered.

We prove that a simple adjoint Chevalley group over a totally disconnected field has no nontrivial pseudocharacters and no bounded nontrivial finite-dimensional quasirepresentations. Therefore, every finite-dimensional quasirepresentation with sufficiently small defect of this group is close to an ordinary representation of the group.

This paper examines the equation of autowave diffusion with a discontinuous source. Conditions are formulated under which an autowave can pass through the interface between media. Here the direction of the autowave’s motion is maintained, while its velocity changes in magnitude. An approximate law of motion of the autowave front is obtained, and an existence theorem is proved. The primary research method is the asymptotic method of differential inequalities. The results of this paper can be used to describe the propagation of autowaves in layered media and to solve inverse problems determining the characteristics of such media. The study of the process of autowave propagation in layered media can be used to develop diverse biophysical models, such as the spatially heterogeneous distribution of populations in habitats, the territorial development of megacities, and patterns of cancer cell proliferation.

The paper studies a wave equation whose velocity has a perturbation localized at a point (x_0). The initial condition has the form of a rapidly oscillating wave packet whose wavelength is not comparable to the scale of the inhomogeneity. Specifically, the length of the initial wave is of the order of (varepsilon) and the width of the localized inhomogeneity is of the order of (varepsilon^{alpha}), where (varepsilon) is a small parameter tending to (0) and (alpha) is any positive number. The cases (alpha<1) and (alpha>1) are considered separately.

An asymptotic expansion with respect to a small parameter of a singularly perturbed system of hyperbolic equations, describing vibrations of two rigidly connected strings is constructed. Under certain conditions imposed on these problems, the principal term of the asymptotic expansion of the solution is described by the generalized Korteweg–de Vries equation.

A new method for determining thermal conductivity coefficients and estimating heat flux densities in nonlinear media using the simulation data has been developed and justified. The method is based on a stable numerical algorithm for solving the inverse problem of reconstructing the unknown parameters of a singularly perturbed model for a stationary nonlinear heat equation with a flux term linearly dependent on the temperature (as an example). This algorithm uses either an asymptotic small-parameter approximation of a stable solution to the direct problem or an information on the position of the internal layer of the thermal structure obtained using an asymptotic analysis in combination with experimental data. Numerical calculations were performed for several innovative and promising types of fuel alloys and mixed nitride nuclear fuel using the parameters of real fuel cores for fast neutron reactors.

A nonlinear partial differential equation describing waves in a convecting fluid with a nonlinear source is considered. Since the Cauchy problem is not solvable by the inverse scattering transform a traveling wave variables is employed to reduce the partial differential equation to fourth-order ordinary differential equation. The Painlevé test is used to derive the parameter constraints of the equation for its integrability. The relationship between the Fuchs indices obtained from the Painlevé test and the form of the first integrals is discussed. Guided by this information the first integrals are constructed. Under four parameter constraints obtained during Painlevé test general solution with four arbitrary constants are found. All such general solutions are expressed in terms of the transcendents of the first Painlev e equation, which are non-classical functions not reducible to known elementary functions.