87 citations · 453 across the 38 of their papers we have counts for
38 papers
One-dimensional relativistic hydrogen-like atom in Dirac materials: Energy spectra and supercritical states
S. Z. Rakhmanov, K. P. Matchonov, A. K. Rakhimov +1
We consider a model of 1D relativistic hydrogen-like atom, formed by a Coulomb impurity in graphene nanoribbon. Describing the electron motion in terms of the one-dimensional Dirac…
Burgers equation on networks: Metric graph based approach
K. K. Sabirov, Kh. Sh. Matyokubov, D. U. Matrasulov
Weconsider Burgers equation on metric graphs for simplest topologies such as star, loops, and tree graphs. Exact traveling wave solutions are obtained for the vertex boundary condi…
Optical high harmonic generation in Dirac materials
S. Rakhmanov, K. Matchonov, H. Yusupov +2
We study high-order harmonic generation by optically driven one- and two-dimensional hydrogenlike atoms formed by Coulomb imurities in graphene. The time-dependent Dirac equations…
Driven transparent quantum graphs
J. R. Yusupov, M. Ehrhardt, Kh. Sh. Matyokubov +1
In this paper, we discuss the concept of quantum graphs with transparent vertices by considering the case where the graph interacts with an external time-independent field. In part…
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…
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…