34 citations · 64 across the 10 of their papers we have counts for
4 papers · 1 filter
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…