2 citations · 5 across the 5 of their papers we have counts for
9 papers
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…
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…
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…