17 citations · 36 across the 14 of their papers we have counts for
15 papers
Matrix representation of Picard--Lefschetz--Pham theory near the real plane in
A. V. Shanin, A. I. Korolkov, N. M. Artemov +1
A matrix formalism is proposed for computations based on Picard--Lefschetz theory in a 2D case. The formalism is essentially equivalent to the computation of the intersection indic…
Recycling solutions of boundary value problems: the Wiener--Hopf perspective on embedding formula
A. I. Korolkov, A. V. Kisil
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 pr…
A note on double Floquet-Bloch transforms and the far-field asymptotics of Green's functions tailored to periodic structures
Andrey V. Shanin, Raphael C. Assier, Andrey I. Korolkov +1
We propose a general procedure to study double integrals arising when considering wave propagation in periodic structures. This method, based on a complex deformation of the integr…
A contribution to the mathematical theory of diffraction. Part II: Recovering the far-field asymptotics of the quarter-plane problem
Raphael C. Assier, Andrey V. Shanin, Andrey I. Korolkov
We apply the stationary phase method developed in (Assier, Shanin \& Korolkov, QJMAM, 76(1), 2022) to the problem of wave diffraction by a quarter-plane. The wave field is written…
A contribution to the mathematical theory of diffraction. Part I: A note on double Fourier integrals
Raphaël C. Assier, Andrey V. Shanin, Andrey I. Korolkov
We consider a large class of physical fields written as double inverse Fourier transforms of some functions of two complex variables. Such integrals occur very often in pra…
Saddle point method for transient processes in waveguides
A. V. Shanin, A. I. Korolkov, K. S. Kniazeva
A modification of the saddle point method is proposed for computation of non-stationary wave processes (pulses) in waveguides. The dispersion diagram of the waveguide is continued…
Diffraction by a Dirichlet right angle on a discrete planar lattice
A. V. Shanin, A. I. Korolkov
A problem of scattering by a Dirichlet right angle on a discrete square lattice is studied. The waves are governed by a discrete Helmholtz equation. The solution is looked for in t…
Transient processes in a gas / plate structure in the case of light gas loading
M. A. Mironov, A. V. Shanin, A. I. Korolkov +1
Problems of pulse excitation in an acoustic waveguide with a flexible wall and in an acoustic half-space with a flexible wall are studied. In both cases the flexible wall is descri…
Asymptotical study of two-layered discrete waveguide with a weak coupling
A. I. Korolkov, A. V. Shanin, K. S. Kniazeva
A thin two-layered waveguide is considered. The governing equations for this waveguide is a matrix Klein--Gordon equation of dimension~2. A formal solution of this system in the fo…
Scalar Klein--Gordon equation and its analytically continued dispersion diagram
A. I. Korolkov, A. V. Shanin
The scalar Klein-Gordon equation describes wave motion in a waveguide with a cut-off. For example, the displacement of an elastic cord anchored to a solid base by elastic elements…
Sommerfeld--type integrals for discrete diffraction problems
A. V. Shanin, A. I. Korolkov
Three problems for a discrete analogue of the Helmholtz equation are studied analytically using the plane wave decomposition and the Sommerfeld integral approach. They are: 1) the…
Diffraction by an elongated body of revolution. A boundary integral equation based on the parabolic equation
A. V. Shanin, A. I. Korolkov
A problem of diffraction by an elongated body of revolution is studied. The incident wave falls along the axis. The wavelength is small comparatively to the dimensions of the body.…
Diffraction of a mode close to its cut-off by a transversal screen in a planar waveguide
Andrey V. Shanin, Andrey I. Korolkov
The problem of diffraction of a waveguide mode by a thin Neumann screen is considered. The incident mode is assumed to have frequency close to the cut-off. The problem is reduced t…
Diffraction by an impedance strip II. Solving Riemann-Hilbert problems by OE-equation method
Andrey V. Shanin, Andrey I. Korolkov
The current paper is the second part of a series of two papers dedicated to 2D problem of diffraction of acoustic waves by a segment bearing impedance boundary conditions. In the f…
Diffraction by an impedance strip I. Reducing diffraction problem to Riemann-Hilbert problems
Andrey V. Shanin, Andrey I. Korolkov
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…