34 citations · 64 across the 10 of their papers we have counts for
11 papers
Discrete PT-symmetric solitons on branched lattices: Vertex states, stability, and vortices
M. Akramov, A. Fayzullaev, O. Tojakhmadova +1
Branching fundamentally modifies nonlinear localization by introducing vertex degrees of freedom absent in one-dimensional lattices. We investigate localized states in a PT-symmetr…
Discrete Dirac equation on quantum graphs: A model of a Dirac particle in a branched lattice
Mashrab Akramov, Carsten Trunk, Davron Matrasulov
We study the one-dimensional time-independent discrete Dirac equation on graphs with discrete edges. Both continuous and discrete formulations of the graphs are considered, with pa…
Transparent boundary conditions for the spatially discrete Schrödinger equation: Reflectionless quantum transport in 1D lattices
Mashrab E. Akramov, Jambul R. Yusupov, Matthias Ehrhardt +1
We construct exact transparent boundary conditions (TBCs) for a time-continuous, spatially discrete Schrödinger equation that models a one-dimensional quantum lattice. Using a rece…
PT-symmetric branched optical lattices: Spectral properties and stability of solitons
O. K. Tojakhmadova, T. Akhmadjanov, M. E. Akramov
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…
Discrete Schrodinger equation on graphs: An effective model for branched quantum lattice
M. Akramov, C. Trunk, J. Yusupov +1
We propose an approach to quantize discrete networks (graphs with discrete edges). We introduce a new exact solution of discrete Schrodinger equation that is used to write the solu…
Transparent PT-symmetric nonlinear networks
Mashrab Akramov, Jambul Yusupov, Matthias Ehrhardt +2
We consider reflectionless wave propagation in networks modeled in terms of the nonlocal nonlinear Schrödinger (NNLS) equation on metric graphs, for which transparent boundary cond…
Discrete sine-Gordon equation on metric graphs: A simple model for Josephson junction networks
M. E. Akramov, J. R. Yusupov, I. N. Askerzade +1
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. Ex…
Transparent boundary conditions for the nonlocal nonlinear Schroedinger equation: A model for reflectionless propagation of PT-symmetric solitons
M. E. Akramov, J. R. Yusupov, M. Ehrhardt +2
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 o…
Discrete Nonlocal Nonlinear Schroedinger equation on Metric Graphs: Dynamics of PT-Symmetric Solitons in Discrete Networks
M. Akramov, F. Khashimova, D. Matrasulov
We consider PT-symmetric, discrete nonlocal nonlinear Schrödinger equation on metric graphs. Soliton solutions are obtained for simplest graph topologies, such as star and tree gra…
Soliton generation in PT-symmetric optical fiber networks
M. E. Akramov, K. K. Sabirov, O. V. Karpova +1
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…
Nonlocal Nonlinear Schrodinger Equation on Metric Graphs
K. Sabirov, D. Matrasulov, M. Akramov +1
We consider PT-symmetric, nonlocal nonlinear Schrodinger equation on metric graphs. Vertex boundary conditions are derived from the conservation laws. Soliton solutions are obtaine…