http://dspace.nbuv.gov.ua:80/handle/123456789/140533 2026-04-19T00:30:03Z http://dspace.nbuv.gov.ua:80/handle/123456789/140552 Solutions of Nonlinear Schrödinger Equation with Two Potential Wells in Linear/Nonlinear Media Gerasimchuk, V.S.; Gerasimchuk, I.V.; Dranik, N.I. In the framework of nonlinear Schrödinger equation, we analytically studied the nonlinear localized states in the system with two potential holes in the cases of linear and nonlinear media in the holes as well as their linear and nonlinear environment. All the possible solutions for the system are found and studied. The frequency dependences of the field amplitudes for all types of possible stationary localized states are obtained. 2016-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/140551 Spherical Quadrilaterals with Three Non-integer Angles Eremenko, A.; Gabrielov, A.; Tarasov, V. A spherical quadrilateral is a bordered surface homeomorphic to a closed disk, with four distinguished boundary points called corners, equipped with a Riemannian metric of constant curvature 1, except at the corners, and such that the boundary arcs between the corners are geodesic. We discuss the problem of classification of these quadrilaterals and perform the classification up to isometry in the case that one corner of a quadrilateral is integer (i.e., its angle is a multiple of π) while the angles at its other three corners are not multiples of π. The problem is equivalent to classification of Heun's equations with real parameters and unitary monodromy, with the trivial monodromy at one of its four singular point. 2016-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/140550 On Stabilization Problem for Nonlinear Systems with Power Principal Part Bebiya, M.O.; Korobov, V.I. In the present paper, the stabilization problem for the uncontrollable with respect to the first approximation nonlinear system with power principal part is solved. A class of stabilizing controls for the nonlinear approximation of this system is constructed by using the Lyapunov function method. It is proved that the same controls solve the stabilization problem for the original nonlinear system. An ellipsoidal approximation of the domain of attraction to the origin is given. 2016-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/140549 Time Frequency Method of Solving One Boundary Value Problem for a Hyperbolic System and Its Application to the Oil Extraction Aliev, F.A.; Aliev, N.A.; Guliev, A.P. We consider the boundary value problem, where the motion of the object is described by the two-dimensional linear system of partial differential equations of hyperbolic type where a discontinuity is at a point within the interval that defines the phase coordinate x. Using the method of series and Laplace transformation in time t (time-frequency method), an analytical solution is found for the determination of debit Q(2l, t) and pressure P(2l, t), which can be effective in the calculation of the coefficient of hydraulic resistance in the lift at oil extraction by gas lift method where l is the well depth. For the case where the boundary functions are of exponential form, the formulas for P(2l, t) and Q(2l, t) depending only on t are obtained. It is shown that at constant boundary functions, these formulas allow us to determine the coefficient of hydraulic resistance in the lift of gas lift wells, which determines the change in the dynamics of pollution. 2016-01-01T00:00:00Z