87 citations · 253 across the 11 of their papers we have counts for
11 papers
Nonlinear standing waves on planar branched systems: Shrinking into metric graph
Z. Sobirov, D. Babajanov, D. Matrasulov
We treat the stationary nonlinear Schroodinger equation on two-dimensional branched domains, so-called fat graphs. The shrinking limit when the domain becomes one-dimensional metri…
Sine-Gordon solitons in networks: Scattering and transmission at vertices
Zarif Sobirov, Doniyor Babajanov, Davron Matrasulov +2
We consider the sine-Gordon equation on metric graphs with simple topologies and derive vertex boundary conditions from the fundamental conservation laws, such as energy and curren…
Soliton transport in tubular networks: transmission at vertices in the shrinking limit
Hannes Uecker, Daniel Grieser, Zarif Sobirov +2
Soliton transport in tube-like networks is studied by solving the nonlinear Schroedinger equation (NLSE) on finite thickness ("fat") graphs. The dependence of the solution and of t…
Bernoulli's formula and Poisson's equations for a confined quantum gas: Effects due to a moving piston
Katsuhiro Nakamura, Zarifboy A. Sobirov, Davron U. Matrasulov +1
We study a nonequilibrium equation of states of an ideal quantum gas confined in the cavity under a moving piston with a small but finite velocity in the case that the cavity wall…
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…
Time dependent neutrino billiards
D. U. Matrasulov, Z. A. Sobirov, Sh. Ataev +1
Quantum dynamica of a massless Dirac particle in time-dependent 1D box and circular billiard with time-dependent radius is studied. An exact analytical wave functions and eigenvalu…
Cauchy Problem for for some high order generalization of Korteweg - de Vries equation
Z. A. Sobirov, S. Abdinazarov
In this work we study Cauchy problem for a high-order differential equation $\frac{\partial u(y,x)}{\partial y}+P(\frac{\partial}{\partial x})u(y,x)=γ\frac{\partial}{\partial x}(u^…
Ideal quantum gas in expanding cavity: nature of non-adiabatic force
K. Nakamura, S. K. Avazbaev, Z. A. Sobirov +2
We consider a quantum gas of non-interacting particles confined in the expanding cavity, and investigate the nature of the non-adiabatic force which is generated from the gas and a…
Transport in simple networks described by integrable discrete nonlinear SchrÄodinger equation
K. Nakamura, Z. A. Sobirov, D. U. Matrasulov +1
We elucidate the case in which the Ablowitz-Ladik (AL) type discrete nonlinear SchrÄodinger equa- tion (NLSE) on simple networks (e.g., star graphs and tree graphs) becomes complet…
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…