17 citations · 36 across the 14 of their papers we have counts for
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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…
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…
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…