arXiv subjects

M. E. Akramov

Publications and source records attributed to M. E. Akramov.

4 recordsLinked to original sources

arXiv2026

PT-symmetric branched optical lattices: Spectral properties and stability of solitons

We investigate branched PT-symmetric optical lattices. We consider both the linear and nonlinear Schrödinger equations with a PT-symmetric periodic potential on the graph and solve them by imposing weighted vertex boundary conditions. A constraint derived from these vertex conditions determines the exceptional point of the system. In the PT unbroken phase, this constraint enforces PT-symmetric boundary conditions at the vertices, ensuring a purely real spectrum; its violation leads to the emergence of complex eigenvalues in the linear regime. In the nonlinear regime, the same constraint determines the linear stability of solitons: satisfying the constraint yields stable solitons, whereas violating it corresponds to unstable solitons.

nlin.PS↗

arXiv2023

Discrete sine-Gordon equation on metric graphs: A simple model for Josephson junction networks

We consider discrete sine-Gordon equation on branched domains. The latter is modeled in terms of the metric graphs with discrete bonds having the form of the branched 1D chains. Exact analytical solutions of the problem are obtained for special case of the constraints given by in terms of simple sum rule. Numerical solution is obtained when the constraint is not fulfilled.

nlin.SI↗

arXiv2022

Transparent boundary conditions for the nonlocal nonlinear Schroedinger equation: A model for reflectionless propagation of PT-symmetric solitons

We consider the problem of reflectionless propagation of PT-symmetric solitons described by the nonlocal nonlinear Schroedinger equation on a line in the framework of the concept of transparent boundary conditions for evolution equations. Transparent boundary conditions for the nonlocal nonlinear Schroedinger equation are derived. The absence of backscattering at the artificial boundaries is confirmed by the numerical implementation of the transparent boundary conditions.

nlin.SI↗

arXiv2022

Soliton generation in PT-symmetric optical fiber networks

We consider the problem of soliton generation in PT-symmetric optical fiber networks, where soliton dynamics is governed by nonlocal nonlinear Schrodinger equation on metric graphs. Exact formulae for the number of generated solitons are derived for the cases, when the problem is integrable. Numerical solutions are obtained for the case, when integrability is broken.

nlin.PS↗