activity
20192026
collaborators

5 papers

math-ph2026

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…

math-ph2023

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…

math-ph2020

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…

math-ph2019

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…

math-ph2019

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…