18 citations · 31 across the 12 of their papers we have counts for
12 papers
Asymptotic forms of the Ursell edge waves on a gently sloping beach
P. Zhevandrov, A. Merzon, M. I. Romero Rodríguez
It is shown that the asymptotics of the Ursell trapping modes on a sloping beach of small slope angle alpha coincide with the inverse Fourier transform of standard WKB exponentials…
Discrete and embedded trapped modes in a plane quantum waveguide with a small obstacle: exact solutions
P. Zhevandrov, A. Merzon, M. I. Romero Rodríguez +1
Exact solutions describing trapped modes in a plane quantum waveguide with a small rigid obstacle are constructed in the form of convergent series in powers of the small parameter…
On Malyshev's method of automorphic functions in diffraction by wedges
Alexander Komech, Anatoli Merzon
We describe Malyshev's method of automorphic functions in application to boundary value problems in angles and to diffraction by wedges. We give a consize survey of related results…
Model BVP problem for the Helmhotz equation in a nonconvex angle with periodic boundary data
A. Merzon, P. Zhevandrov, M. I. Romero Rodríguez +1
In the presented work, we solve the Dirichlet boundary problem for the Helmholtz equation in an exterior angle with periodic boundary data. We prove the existence and uniqueness of…
Trapped modes and resonances for thin horizontal cylinders in a two-layer fluid
P. Zhevandrov, A. Merzon, M. I. Romero Rodríguez +1
Exact solutions of the linear water-wave problem describing oblique waves over a submerged horizontal cylinder of small (but otherwise fairly arbitrary) cross-section in a two-laye…
Time-dependent approach to the uniqueness of the Sommerfeld solution of the diffraction problem by a half-plane
A. Merzon, P. Zhevandrov, J. E. De la Paz Méndez +1
We consider the Sommerfeld problem of diffraction by an opaque half-plane with a real wavenumber interpreting it as the limiting case, as time tends to infinity, of the correspondi…
Wave scattering by a periodic perturbation: embedded Rayleigh-Bloch modes and resonances
P. Zhevandrov, A. Merzon, M. I. Romero Rodríguez +1
The scattering of quasiperiodic waves for a two-dimensional Helmholtz equation with a constant refractive index perturbed by a function which is periodic in one direction and of fi…
Rayleigh-Bloch waves trapped by a periodic perturbation: exact solutions
A. Merzon, P. Zhevandrov, M. I. Romero Rodríguez +1
Exact solutions describing the Rayleigh-Bloch waves for the two-dimensional Helmholtz equation are constructed in the case when the refractive index is a sum of a constant and a sm…
On justification of Sobolev's formula for diffraction by wedge
A. I. Komech, A. E. Merzon, J. E. De la Paz Mendez
We consider the scattering of an arbitary incident plane wave which is a tempered distribution by a two-dimensional wedge.
An explicit formula for the nonstationary diffracted wave scattered on a NN-wedge
Anel Esquivel Navarrete, Anatoli Merzon
We consider two dimensional nonstationary scattering of plane waves by a NN-wedge. We prove the existence and uniqueness of a solution to the corresponding mixed problem and we giv…
On Asymptotic Completeness of Scattering in the Nonlinear Lamb System, II
A. I. Komech, A. E. Merzon
We establish the asymptotic completeness in the nonlinear Lamb system for hyperbolic stationary states. For the proof we construct a trajectory of a reduced equation (which is a no…
Hausdorff-Young type theorems for the Laplace transform restricted to a ray or to a curve in the complex plane
Anatoli Merzon, Sergey Sadov
Let p and q be conjugate exponents, with p in [1,2]. It is shown that the Laplace transform acts boundedly between the Lp space with unit weight on the positive real semiaxis and t…