5 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…
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…