23 citations · 88 across the 23 of their papers we have counts for
6 papers · 1 filter
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…