Bibigul Omarova - Academia.edu (original) (raw)

Papers by Bibigul Omarova

Research paper thumbnail of On Multiperiodic Solutions of Perturbed Nonlinear Autonomous Systems with the Differentiation Operator on a Vector Field

The Eurasian Mathematical Journal (EMJ) publishes carefully selected original research papers in ... more The Eurasian Mathematical Journal (EMJ) publishes carefully selected original research papers in all areas of mathematics written by mathematicians, principally from Europe and Asia. However papers by mathematicians from other continents are also welcome. From time to time the EMJ publishes survey papers. The EMJ publishes 4 issues in a year. The language of the paper must be English only. The contents of the EMJ are indexed in Scopus, Web of Science (ESCI), Mathematical Reviews, MathSciNet, Zentralblatt Math (ZMATH), Referativnyi Zhurnal-Matematika, Math-Net.Ru. The EMJ is included in the list of journals recommended by the Committee for Control of Education and Science (Ministry of Education and Science of the Republic of Kazakhstan) and in the list of journals recommended by the Higher Attestation Commission (Ministry of Education and Science of the Russian Federation).

Research paper thumbnail of Research of Multiperiodic Solutions of Perturbed Linear Autonomous Systems with Differentiation Operator on the Vector Field

PHYSICO-MATHEMATICAL SERIES

A linear system with a differentiation operator D with respect to the directions of vector fields... more A linear system with a differentiation operator D with respect to the directions of vector fields of the form of the Lyapunov's system with respect to space independent variables and a multiperiodic toroidal form with respect to time variables is considered. All input data of the system multiperiodic depend on time variables or do not depend on them. The autonomous case of the system was considered in our early work. In this case, some input data received perturbations depending on time variables. We study the question of representing the required motion described by the system in the form of a superposition of individual periodic motions of rationally incommensurable frequencies. The initial problems and the problems of multiperiodicity of motions are studied. It is known that when determining solutions to problems, the system integrates along the characteristics outgoing from the initial points, and then, the initial data is replaced by the first integrals of the characteristic systems. Thus, the required solution consists of the following components: characteristics and first integrals of the characteristic systems of operator D, the matricant and the free term of the system itself. These components, in turn, have periodic and non-periodic structural components, which are essential in revealing the multiperiodic nature of the movements described by the system under study. The representation of a solution with the selected multiperiodic components is called the multiperiodic structure of the solution. It is realized on the basis of the well-known Bohr's theorem on the connection of a periodic function of many variables and a quasiperiodic function of one variable. Thus, more specifically, the multiperiodic structures of general and multiperiodic solutions of homogeneous and inhomogeneous systems with perturbed input data are investigated. In this spirit, the zeros of the operator D and the matricant of the system are studied. The conditions for the absence and existence of multiperiodic solutions of both homogeneous and inhomogeneous systems are established.

Research paper thumbnail of Periodic solution of a single system of differential equations in partial derivatives

International Journal of ADVANCED AND APPLIED SCIENCES

The main difficulty of the Cauchy equation is that there is no domain in which the desired soluti... more The main difficulty of the Cauchy equation is that there is no domain in which the desired solution must be determined. This situation leads to the complexity of finding the answer. The study presents a solution of the Cauchy problem at any values. The achievement of the set goal will enable solving one of the key problems of gas dynamics. To that end, it is necessary to define the solution, since a solution in a classical form is nonexistent for this type of equations. We presented an algorithm for the construction of periodic, in terms of variables, solutions of the system in first order partial derivatives. The study found a sufficient condition of existence of periodic, in terms of variables, solutions in the broad sense of differential equation systems in partial derivatives.

Research paper thumbnail of On Multiperiodic Solutions of Perturbed Nonlinear Autonomous Systems with the Differentiation Operator on a Vector Field

The Eurasian Mathematical Journal (EMJ) publishes carefully selected original research papers in ... more The Eurasian Mathematical Journal (EMJ) publishes carefully selected original research papers in all areas of mathematics written by mathematicians, principally from Europe and Asia. However papers by mathematicians from other continents are also welcome. From time to time the EMJ publishes survey papers. The EMJ publishes 4 issues in a year. The language of the paper must be English only. The contents of the EMJ are indexed in Scopus, Web of Science (ESCI), Mathematical Reviews, MathSciNet, Zentralblatt Math (ZMATH), Referativnyi Zhurnal-Matematika, Math-Net.Ru. The EMJ is included in the list of journals recommended by the Committee for Control of Education and Science (Ministry of Education and Science of the Republic of Kazakhstan) and in the list of journals recommended by the Higher Attestation Commission (Ministry of Education and Science of the Russian Federation).

Research paper thumbnail of Research of Multiperiodic Solutions of Perturbed Linear Autonomous Systems with Differentiation Operator on the Vector Field

PHYSICO-MATHEMATICAL SERIES

A linear system with a differentiation operator D with respect to the directions of vector fields... more A linear system with a differentiation operator D with respect to the directions of vector fields of the form of the Lyapunov's system with respect to space independent variables and a multiperiodic toroidal form with respect to time variables is considered. All input data of the system multiperiodic depend on time variables or do not depend on them. The autonomous case of the system was considered in our early work. In this case, some input data received perturbations depending on time variables. We study the question of representing the required motion described by the system in the form of a superposition of individual periodic motions of rationally incommensurable frequencies. The initial problems and the problems of multiperiodicity of motions are studied. It is known that when determining solutions to problems, the system integrates along the characteristics outgoing from the initial points, and then, the initial data is replaced by the first integrals of the characteristic systems. Thus, the required solution consists of the following components: characteristics and first integrals of the characteristic systems of operator D, the matricant and the free term of the system itself. These components, in turn, have periodic and non-periodic structural components, which are essential in revealing the multiperiodic nature of the movements described by the system under study. The representation of a solution with the selected multiperiodic components is called the multiperiodic structure of the solution. It is realized on the basis of the well-known Bohr's theorem on the connection of a periodic function of many variables and a quasiperiodic function of one variable. Thus, more specifically, the multiperiodic structures of general and multiperiodic solutions of homogeneous and inhomogeneous systems with perturbed input data are investigated. In this spirit, the zeros of the operator D and the matricant of the system are studied. The conditions for the absence and existence of multiperiodic solutions of both homogeneous and inhomogeneous systems are established.

Research paper thumbnail of Periodic solution of a single system of differential equations in partial derivatives

International Journal of ADVANCED AND APPLIED SCIENCES

The main difficulty of the Cauchy equation is that there is no domain in which the desired soluti... more The main difficulty of the Cauchy equation is that there is no domain in which the desired solution must be determined. This situation leads to the complexity of finding the answer. The study presents a solution of the Cauchy problem at any values. The achievement of the set goal will enable solving one of the key problems of gas dynamics. To that end, it is necessary to define the solution, since a solution in a classical form is nonexistent for this type of equations. We presented an algorithm for the construction of periodic, in terms of variables, solutions of the system in first order partial derivatives. The study found a sufficient condition of existence of periodic, in terms of variables, solutions in the broad sense of differential equation systems in partial derivatives.