Related papers: Diffraction by an impedance strip II. Solving Riem…
A 2D problem of acoustic wave scattering by a segment bearing impedance boundary conditions is considered. In the current paper (the first part of a series of two) some preliminary steps are made, namely, the diffraction problem is reduced…
A novel approach to Riemann--Hilbert problems of particular class is introduced. The approach is applicable to problems in which the multiplicative jump is set on a half-line. Such problems are linked to some Wiener--Hopf problems motivated…
The diffraction of a plane wave by a transversely inhomogeneous isotropic nonmagnetic linearly polarized dielectric layer filled with a Kerr-type nonlinear medium is considered. The analytical and numerical solution techniques are…
Scattering of a plane electromagnetic wave by an anisotropic impedance right-angled concave wedge at skew incidence is analyzed. A closed-form solution is derived by reducing the problem to a symmetric order-2 vector Riemann-Hilbert problem…
Two boundary value problems for the Helmholtz equation in a semi-infinite strip are considered. The main feature of these problems is that, in addition to the function and its normal derivative on the boundary, the functionals of the…
On an example of the open nonlinear electrodynamic system - transverse non-homogeneous, isotropic, nonlinear (a Kerr-like dielectric nonlinearity) dielectric layer, the algorithms of solution of the diffraction problem of a plane wave on…
Analytical methods are fundamental in studying acoustics problems. One of the important tools is the Wiener-Hopf method, which can be used to solve many canonical problems with sharp transitions in boundary conditions on a plane/plate.…
A matrix factorization problem is considered. The matrix to be factorized is algebraic, has dimension 2 X 2 and belongs to Moiseev's class. A new method of factorization is proposed. First, the matrix factorization problem is reduced to a…
The paper continues the analysis, started in [1] (Part I,arXiv:2302.04353), of the model open wave-guide problem defined by 2 semi-infinite, rectangular wave-guides meeting along a common perpendicular line. In Part I we reduce the solution…
The problem of plane-wave diffraction on semi-infinite orthorhombic electromagnetic (photonic) crystals of general kind is considered. Boundary conditions are obtained in the form of infinite system of equations relating amplitudes of…
Based upon elements of the modern Pseudoanalytic Function Theory, we analyse a new method for numerically approaching the solution of the Dirichlet boundary value problem, corresponding to the two-dimensional Electrical Impedance Equation.…
In this paper, we revisit the classic problem of diffraction of electromagnetic waves by an aperture in a perfectly conducting plane. We formulate the diffraction problem using a boundary integral equation that is defined on the aperture…
Embedding formula allows to recycle solution of a family boundary value problems by expressing all the solutions in terms of a small number of solutions. Such formulas have been previously derived in the context of diffraction by applying a…
This article considers the problem of diffraction by a wedge consisting of two semi-infinite periodic arrays of point scatterers. The solution is obtained in terms of two coupled systems, each of which is solved using the discrete…
The diffraction of a scalar plane wave from a doubly-periodic surface on which either the Dirichlet or Neumann boundary condition is imposed is studied by means of a rigorous numerical solution of the Rayleigh equation for the amplitudes of…
We analyze an initial-boundary value problem for the Ostrovsky-Vakhnenko equation on the half-line. This equation can be viewed as the short wave model for the Degasperis-Procesi (DP) equation. We show that the solution u(x,t) can be…
In this paper we study the variational method and integral equation methods for a conical diffraction problem for imperfectly conducting gratings modeled by the impedance boundary value problem of the Helmholtz equation in periodic…
Traditionally, the diffraction of a scalar wave satisfying Helmholtz equation through an aperture on an otherwise black screen can be solved approximately by Kirchhoff's integral over the aperture. Rubinowicz, on the other hand, was able to…
This paper considers to the problems of diffraction of electromagnetic waves on a half-plane, which has a finite inclusion in the form of a Lipschitz curve. The diffraction problem formulated as boundary value problem for Helmholtz…
Scalar wave scattering by many small particles with impedance boundary condition and creating material with a desired refraction coefficient are studied. The acoustic wave scattering problem is solved asymptotically and numerically under…