We consider a system of differential equations that describes the dynamics of an infinite system ... more We consider a system of differential equations that describes the dynamics of an infinite system of nonlinearly coupled nonlinear oscillators on the 2D lattice. By the method of critical points, we obtain a result on the existence of solitary traveling waves.
By using the method of critical points and the concentration-compactness principle, we study the ... more By using the method of critical points and the concentration-compactness principle, we study the problem of existence of heteroclinic traveling waves for a system of linearly coupled nonlinear oscillators on a two-dimensional lattice.
It is considered the system of differential equations that describes the dynamics of an infinite ... more It is considered the system of differential equations that describes the dynamics of an infinite system of linearly coupled nonlinear oscillators on 2D-lattice. Results on existence of the periodic travelling waves are obtained. C. Н. Бак. Условия существования периодических бегущих волн в системе нелинейных осцилляторов на двумерной решетке // Мат. Студiї.-2011.-Т.35, №1.-C.60-65. Рассматривается система дифференциальных уравнений, описывающая динамику бесконечной системы линейно связанных нелинейных осцилляторов на двумерной решетке. Получен результат о существовании периодических бегущих волн.
It is considered the system of differential equations that describes the dynamics of an infinite ... more It is considered the system of differential equations that describes the dynamics of an infinite system of linearly coupled nonlinear oscillators on 2D-lattice. Results on existence of the periodic travelling waves are obtained. C. Н. Бак. Условия существования периодических бегущих волн в системе нелинейных осцилляторов на двумерной решетке // Мат. Студiї.-2011.-Т.35, №1.-C.60-65. Рассматривается система дифференциальных уравнений, описывающая динамику бесконечной системы линейно связанных нелинейных осцилляторов на двумерной решетке. Получен результат о существовании периодических бегущих волн.
Mathematical and computer modelling. Series: Physical and mathematical sciences, 2020
This article is devoted to the study of an infinite-dimensional Hamiltonian system, which describ... more This article is devoted to the study of an infinite-dimensional Hamiltonian system, which describes an infinite system of linearly coupled nonlinear oscillators on a two-dimensional lattice. This system is a counteble system of ordinary differential equations. It is convenient to consider this system as a differential-operator equation in Hilbert space of real two-way sequences. The problem of existence of periodic solutions for such systems with power potential is considered. The main conditions for the existence of these solutions are the spatial periodicity of the coefficients of the linear interaction of oscillators and the positivity of this operator. This article shows that periodic solutions can be constructed using the constained minimization method. For this, a functional is constructed whose critical points are the desired periodic solutions. This functional is represented as the difference between the quadratic and non-quadratic parts. Next, we consider the problem of con...
The Fermi-Pasta-Ulam-type systems with saturable nonlinearities, namely, infinite systems of part... more The Fermi-Pasta-Ulam-type systems with saturable nonlinearities, namely, infinite systems of particles on a two dimensional lattice, have been considered. The main result concerns the existence of traveling-wave solutions with periodic relative displacement profiles. By means of critical point theory, sufficient conditions for the existence of such solutions have been obtained.
The article deals with the Fermi-Pasta-Ulam-type systems that describe infinite systems of partic... more The article deals with the Fermi-Pasta-Ulam-type systems that describe infinite systems of particles on a 2D lattice. The main result concerns the existence of the solutions corresponding to traveling waves with periodic and vanishing profiles. By means of the critical point theory, the sufficient conditions for the existence of such solutions are obtained.
The article deals with the Fermi–Pasta–Ulam type systems with saturable nonlinearities that descr... more The article deals with the Fermi–Pasta–Ulam type systems with saturable nonlinearities that describes an infinite systems of particles on a two dimensional lattice. The main result concerns the existence of solitary traveling waves solutions with vanishing relative displacement profiles. By means of critical point theory, we obtain sufficient conditions for the existence of such solutions.
We consider a system of differential equations that describes the dynamics of an infinite system ... more We consider a system of differential equations that describes the dynamics of an infinite system of nonlinearly coupled nonlinear oscillators on the 2D lattice. By the method of critical points, we obtain a result on the existence of solitary traveling waves.
By using the method of critical points and the concentration-compactness principle, we study the ... more By using the method of critical points and the concentration-compactness principle, we study the problem of existence of heteroclinic traveling waves for a system of linearly coupled nonlinear oscillators on a two-dimensional lattice.
It is considered the system of differential equations that describes the dynamics of an infinite ... more It is considered the system of differential equations that describes the dynamics of an infinite system of linearly coupled nonlinear oscillators on 2D-lattice. Results on existence of the periodic travelling waves are obtained. C. Н. Бак. Условия существования периодических бегущих волн в системе нелинейных осцилляторов на двумерной решетке // Мат. Студiї.-2011.-Т.35, №1.-C.60-65. Рассматривается система дифференциальных уравнений, описывающая динамику бесконечной системы линейно связанных нелинейных осцилляторов на двумерной решетке. Получен результат о существовании периодических бегущих волн.
It is considered the system of differential equations that describes the dynamics of an infinite ... more It is considered the system of differential equations that describes the dynamics of an infinite system of linearly coupled nonlinear oscillators on 2D-lattice. Results on existence of the periodic travelling waves are obtained. C. Н. Бак. Условия существования периодических бегущих волн в системе нелинейных осцилляторов на двумерной решетке // Мат. Студiї.-2011.-Т.35, №1.-C.60-65. Рассматривается система дифференциальных уравнений, описывающая динамику бесконечной системы линейно связанных нелинейных осцилляторов на двумерной решетке. Получен результат о существовании периодических бегущих волн.
Mathematical and computer modelling. Series: Physical and mathematical sciences, 2020
This article is devoted to the study of an infinite-dimensional Hamiltonian system, which describ... more This article is devoted to the study of an infinite-dimensional Hamiltonian system, which describes an infinite system of linearly coupled nonlinear oscillators on a two-dimensional lattice. This system is a counteble system of ordinary differential equations. It is convenient to consider this system as a differential-operator equation in Hilbert space of real two-way sequences. The problem of existence of periodic solutions for such systems with power potential is considered. The main conditions for the existence of these solutions are the spatial periodicity of the coefficients of the linear interaction of oscillators and the positivity of this operator. This article shows that periodic solutions can be constructed using the constained minimization method. For this, a functional is constructed whose critical points are the desired periodic solutions. This functional is represented as the difference between the quadratic and non-quadratic parts. Next, we consider the problem of con...
The Fermi-Pasta-Ulam-type systems with saturable nonlinearities, namely, infinite systems of part... more The Fermi-Pasta-Ulam-type systems with saturable nonlinearities, namely, infinite systems of particles on a two dimensional lattice, have been considered. The main result concerns the existence of traveling-wave solutions with periodic relative displacement profiles. By means of critical point theory, sufficient conditions for the existence of such solutions have been obtained.
The article deals with the Fermi-Pasta-Ulam-type systems that describe infinite systems of partic... more The article deals with the Fermi-Pasta-Ulam-type systems that describe infinite systems of particles on a 2D lattice. The main result concerns the existence of the solutions corresponding to traveling waves with periodic and vanishing profiles. By means of the critical point theory, the sufficient conditions for the existence of such solutions are obtained.
The article deals with the Fermi–Pasta–Ulam type systems with saturable nonlinearities that descr... more The article deals with the Fermi–Pasta–Ulam type systems with saturable nonlinearities that describes an infinite systems of particles on a two dimensional lattice. The main result concerns the existence of solitary traveling waves solutions with vanishing relative displacement profiles. By means of critical point theory, we obtain sufficient conditions for the existence of such solutions.
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