87 citations · 301 across the 24 of their papers we have counts for
24 papers
Kink-antikink soliton solutions of the nonlinear Klein-Gordon equation on branched structures
Q. U. Asadov, K. K. Sabirov, J. R. Yusupov
In this paper, we investigate the nonlinear Klein-Gordon equation on a metric star graph with three semi-infinite bonds. At the branching point, we impose a weighted continuity con…
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…
A derivation of boundary conditions for the space-fractional operator with order at the vertices of metric graphs
K. K. Sabirov, R. R. Ashurov
We consider the space-fractional operator with order on the metric star graph. The boundary conditions at the vertices of the metric star graph providing the self-adjointne…
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…
Fokker-Planck equation on metric graphs
Jasur Matrasulov, Karimjon Sabirov
We consider the Fokker-Planck equation on metric graphs. Vertex boundary conditions are imposed in the form of weight continuity and the probability current conservation. Exact sol…
Reflectionless propagation of Manakov solitons on a line:A model based on the concept of transparent boundary conditions
K. K. Sabirov, J. R. Yusupov, M. M. Aripov +2
We consider the problem of absence of backscattering in the transport of Manakov solitons on a line. The concept of transparent boundary conditions is used for modeling the reflect…
Transparent boundary conditions for the sine-Gordon equation:Modeling the reflectionless propagation of kink solitons on a line
K. K. Sabirov, J. R. Yusupov, M. Ehrhardt +1
We consider the reflectionless transport of sine-Gordon solitons on a line. Transparent boundary conditions for the sine-Gordon equation on a line are derived using the so-called p…
Dirac particles on periodic quantum graphs
J. R. Yusupov, K. K. Sabirov, D. U. Matrasulov
We consider the Dirac equation on periodic networks (quantum graphs). The self-adjoint quasi periodic boundary conditions are derived. The secular equation allowing us to find the…
Dirac Particles in Transparent Quantum Graphs: Tunable transport of relativistic quasiparticles in branched structures
J. R. Yusupov, K. K. Sabirov, Q. U. Asadov +2
We consider the dynamics of relativistic spin-half particles in quantum graphs with transparent branching points. The system is modeled by combining the quantum graph concept with…
Branched Josephson junctions: Current carrying solitons in external magnetic fields
K. Sabirov, D. Babajanov, D. Matrasulov +1
We consider branched Josephson junction created by planar superconductors connected to each other through the Y-junction insulator. Assuming that the structure interacts with the e…
Exciton dynamics in branched conducting polymers: Quantum graphs based approach
J. R. Yusupov, Kh. Matyakubov, K. K. Sabirov +1
We consider dynamics of excitons in branched conducting polymers. An effective model based on the use of quantum graph concept is applied for computing of exciton migration along t…
Transparent nonlinear networks
J. R. Yusupov, K. K. Sabirov, M. Ehrhardt +1
We consider the reflectionless transport of solitons in networks. The system is modeled in terms of the nonlinear Schrödinger equation on metric graphs, for which transparent bound…
Networks with point like nonlinearities
K. K. Sabirov, J. R. Yusupov, H. Susanto +1
We study static nonlinear waves in networks described by a nonlinear Schrodinger equation with point-like nonlinearities on metric graphs. Explicit solutions fulfilling vertex boun…
Transparent Quantum Graphs
J. R. Yusupov, K. K. Sabirov, M. Ehrhardt +1
We consider quantum graphs with transparent branching points. To design such networks, the concept of transparent boundary conditions is applied to the derivation of the vertex bou…
Soliton generation in optical fiber networks
K. K. Sabirov, M. Akromov, Sh. R. Otajonov +1
We consider the problem of soliton generation in branched optical fibers. A model based on the nonlinear Schrodinger equation on metric graphs is proposed. Number of generated soli…
Thermal diffusion in branched structures: Metric graph based approach
K. Sabirov, Zh. Zhunussova, D. Babajanov +1
We consider the problem of heat diffusion in branched systems and networks on the basis of a model described in terms of heat equation on metric graphs. Using the explicit analytic…
PT-symmetric quantum graphs
D. U. Matrasulov, K. K. Sabirov, J. R. Yusupov
We consider branched quantum wires, whose connection rules provide PT-symmetry for the Schrodinger equation on graph. For such PT-symmetric quantum graph we derive general boundary…
Bogoliubov de Gennes equation on metric graphs
K. K. Sabirov, D. Jumanazarov, J. Yusupov +1
We consider Bogoliubov de Gennes equation on metric graphs. The vertex boundary conditions providing self-adjoint realization of the Bogoliubov de Gennes operator on a metric star…
Dynamics of Dirac solitons in networks
K. K. Sabirov, D. B. Babajanov, D. U. Matrasulov +1
We study dynamics of Dirac solitons in prototypical networks modeling them by the nonlinear Dirac equation on metric graphs. Soliton solutions of the nonlinear Dirac equation on si…
The stationary sine-Gordon equation on metric graphs: Exact analytical solutions for simple topologies
K. Sabirov, S. Rakhmanov, D. Matrasulov +1
We consider the stationary sine-Gordon equation on metric graphs with simple topologies. The vertex boundary conditions are provided by flux conservation and matching of derivative…
Time-dependent quantum graph
D. U. Matrasulov, J. R. Yusupov, K. K. Sabirov +1
In this paper we study quantum star graphs with time-dependent bond lengths. Quantum dynamics is treated by solving Schrodinger equation with time-dependent boundary conditions giv…
Stationary Nonlinear Schrödinger Equation on Simplest Graphs: Boundary conditions and exact solutions
Z. A. Sobirov, K. K. Sabirov, D. U. Matrasulov
We treat the stationary (cubic) nonlinear Schrödinger equation (NSLE) on simplest graphs. Formulation of the problem and exact analytical solutions of NLSE are presented for star g…
Soliton solutions of nonlinear Schroedinger equation on simple networks
Z. Sobirov, D. Matrasulov, K. Sabirov +2
We show soliton solutions of nonlinear Schroedinger equation on simple networks consisting of vertices and bonds, where the strength of cubic nonlinearity is different from bond to…