23 citations · 88 across the 23 of their papers we have counts for
26 papers
Plane wave representations for wave scattering on a sphere
Valentin D. Kunz, Andrey V. Shanin, Raphael C. Assier
Motivated by three-dimensional wave diffraction by conical shapes, we consider the two-dimensional problem of wave scattering on the real sphere resulting from a po…
Plane-wave representation for the Laplace--Beltrami equation on a sphere. Application to the Green's function
Andrey V. Shanin, Valentin D. Kunz, Raphael C. Assier
We propose an extension of the plane-wave representation for wave fields defined on the real sphere . This representation is well-known in the planar setting but has…
Asymptotic evaluation of three-dimensional integrals with singularities in application to wave phenomena
A. V. Shanin, A. Yu. Laptev
We consider a three-dimensional Fourier integral in which the exponent in the exponential factor is the product of some phase function and a large parameter. The asymptotics of thi…
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…
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…
Analytical continuation of two-dimensional wave fields
Raphael C. Assier, Andrey V. Shanin
Wave fields obeying the 2D Helmholtz equation on branched surfaces (Sommerfeld surfaces) are studied. Such surfaces appear naturally as a result of applying the reflection method 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…
Vertex Green's functions of a quarter-plane. Links between the functional equation, additive crossing and Lamé functions
Raphaël C. Assier, Andrey V. Shanin
In our previous work (Assier \& Shanin, QJMAM, 2019), we gave a new spectral formulation in two complex variables associated with the problem of plane-wave diffraction by a quarter…
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 a quarter-plane. Analytical continuation of spectral functions
R. C. Assier, A. V. Shanin
The problem of diffraction by a Dirichlet quarter-plane (a flat cone) in a 3D space is studied. The Wiener-Hopf equation for this case is derived and involves two unknown (spectral…
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.…
Transient phenomena in a three-layer waveguide and the analytical structure of the dispersion diagram
A. V. Shanin, K. S. Knyazeva
Excitation of waves in a three-layer acoustic wavegide is studied. The wave field is presented as a sum of integrals. The summation is held over all waveguide modes. The integratio…
A New Numerical Method for Solving the Acoustic Radiation Problem
J. Poblet-Puig, A. V. Shanin
A numerical method of solving the problem of acoustic wave radiation in the presence of a rigid scatterer is described. It combines the finite element method and the boundary algeb…
First arriving signals in layered waveguides. An approach based on dispersion diagrams
Andrey V. Shanin
The first arriving signal (FAS) in a layered waveguide is investigated. It is well known that the velocity of such a signal is close to the velocity of the fastest medium in the wa…
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…
Wiener-Hopf matrix factorization using ordinary differential equations in the commutative case
A. V. Shanin
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 propose…