Zobrazeno 1 - 10
of 118
pro vyhledávání: '"P. Zhevandrov"'
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 characterizing the smallness of the obstacle. The terms of this series
Externí odkaz:
http://arxiv.org/abs/2312.08480
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 solution in an appropriate funcional class and we give an explicit fo
Externí odkaz:
http://arxiv.org/abs/2208.13130
Publikováno v:
Journal of Applied Mathematics, Vol 2007 (2007)
As is well known, submerged horizontal cylinders can serve as waveguides for surface water waves. For large values of the wavenumber k in the direction of the cylinders, there is only one trapped wave. We construct asymptotics of these trapped modes
Externí odkaz:
https://doaj.org/article/f44b60808d82424eb42d80f14d78c226
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-layer fluid are constructed in the form of convergent series in powers of
Externí odkaz:
http://arxiv.org/abs/2011.10156
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 corresponding time-dependent diffraction problem. We prove that the Sommerfeld fo
Externí odkaz:
http://arxiv.org/abs/1908.01663
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 finite support in the other is considered. The scattering problem is uni
Externí odkaz:
http://arxiv.org/abs/1908.00363
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 small amplitude function which is periodic in one direction and of finit
Externí odkaz:
http://arxiv.org/abs/1711.10083
We have studied the emergence of bound states in weakly deformed and/or heterogeneous waveguides, comparing the analytical predictions obtained using a recently developed perturbative method, with precise numerical results, for different configuratio
Externí odkaz:
http://arxiv.org/abs/1605.08126
Publikováno v:
Contemporary Mathematics. Fundamental Directions. 68:653-670
In the present work, we give an explicit solution of the Dirichlet boundary-value problem for the Helmholtz equation in a nonconvex angle with periodic boundary data. We present uniqueness and existence theorems in an appropriate functional class and
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::bee2c51c10b2e864a92c56a3076a6d6c
https://doi.org/10.22363/2413-3639-2022-68-4-653-670
https://doi.org/10.22363/2413-3639-2022-68-4-653-670
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