Zobrazeno 1 - 10
of 175
pro vyhledávání: '"Borisov, D. I."'
Autor:
Borisov, D. I., Zezyulin, D. A.
Publikováno v:
Annals of Physics 459, 169498 (2023)
It has been recently shown that complex two-dimensional (2D) potentials $V_\varepsilon(x,y)=V(y+\mathrm{i}\varepsilon\eta(x))$ can be used to emulate non-Hermitian matrix gauge fields in optical waveguides. Here $x$ and $y$ are the transverse coordin
Externí odkaz:
http://arxiv.org/abs/2310.12549
Autor:
Borisov, D. I.
We consider a boundary value problem for a general second order linear equation in a perforated domain. The perforation is made by small cavities, a minimal distance between the cavities is also small. We impose minimal natural geometric conditions o
Externí odkaz:
http://arxiv.org/abs/2210.12749
Autor:
Borisov, D. I.
We consider a general second order matrix operator in a multi-dimensional domain subject to a classical boundary condition. This operator is perturbed by a first order differential operator, the coefficients of which depend arbitrarily on a small mul
Externí odkaz:
http://arxiv.org/abs/2206.09331
Autor:
Borisov, D. I., Kriz, J.
We consider a general second order linear elliptic equation in a finely perforated domain. The shapes of cavities and their distribution in the domain are arbitrary and non-periodic; they are supposed to satisfy minimal natural geometric conditions.
Externí odkaz:
http://arxiv.org/abs/2204.04829
In the work we consider a boundary value problem for a second order equation with variable coefficients in a multi-dimensional domain perforated by small cavities closely spaced along a given manifold. We assume that the linear sizes of all cavities
Externí odkaz:
http://arxiv.org/abs/2202.10767
Autor:
Borisov, D. I.
We consider an arbitrary metric graph, to which we glue another graph with edges of lengths proportional to $\varepsilon$, where $\varepsilon$ is a small positive parameter. On such graph, we consider a general self-adjoint second order differential
Externí odkaz:
http://arxiv.org/abs/2102.12958
Autor:
Borisov, D. I., Golovina, A. M.
We consider a general elliptic operator in an infinite multi-dimensional cylinder with several distant perturbations; this operator is obtained by ``gluing'' several single perturbation operators $\mathcal{H}^{(k)}$, $k=1,\ldots,n$, at large distance
Externí odkaz:
http://arxiv.org/abs/2008.07289
Publikováno v:
Studies in Applied Mathematics 146, 834-880 (2021)
We consider the operator $${\cal H} = {\cal H}' -\frac{\partial^2\ }{\partial x_d^2} \quad\text{on}\quad\omega\times\mathbb{R}$$ subject to the Dirichlet or Robin condition, where a domain $\omega\subseteq\mathbb{R}^{d-1}$ is bounded or unbounded. Th
Externí odkaz:
http://arxiv.org/abs/2007.02258
Autor:
Borisov, D. I., Zezyulin, D. A.
Publikováno v:
Applied Mathematics Letters 100, 106049 (2020)
We consider a Schroedinger operator on the axis with a bipartite potential consisting of two compactly supported complex-valued functions, whose supports are separated by a large distance. We show that this operator possesses a sequence of approximat
Externí odkaz:
http://arxiv.org/abs/1908.06384
Autor:
Borisov, D. I., Zezyulin, D. A.
Publikováno v:
J. Phys. A: Math. Theor. 52, 445202 (2019)
We consider a parity-time ($\mathcal{PT}$-) symmetric waveguide consisting of a localized gain and loss elements separated by a variable distance. The situation is modelled by a Schr\"odiner operator with localized complex $\mathcal{PT}$-symmetric po
Externí odkaz:
http://arxiv.org/abs/1908.06383