Ognyan Christov
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Ognyan Christov has a total of 7 co-authors. Here are the top co-authors by number of shared publications:
- Sevdzhan Hakkaev
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria
2 shared publications Atanas G. Stefanov
1 shared publication- Atanas Stefanov
Department of Mathematics, University of Alabama - Birmingham, Birmingham, USA
1 shared publication - Georgi Georgiev
Faculty of Mathematics and Informatics, Sofia University "St. Kliment Ohridski'', 5 James Bourchier Blvd., 1164 Sofia, Bulgaria, Bulgaria
1 shared publication - Seungly Oh
Department of Mathematics, Western New England University, Springfield, USA
1 shared publication - Seungly Oh
Department of Mathematics, Western New England University, 1215 Wilbraham Road, Springfield, Massachusetts 01119, USA
1 shared publication
Latest Publications
- Open Access
Semi-Global Symplectic Invariant of the Champagne Bottle
We study a two degrees of freedom Hamiltonian system describing the motion of a particle in a potential field in the form of a symmetric double well, namely , known also as a champagne bottle potential. This system is completely integrable. The champagne bottle is the simplest member of a class of integrable systems that have no global action variables due to a non-trivial monodromy. Beyond that, the geometric and dynamical properties of the system near the equilibrium are of primary interest. We calculate the Birkhoff normal form and the nontrivial action near the focus–focus singularity and obtain the semi-global symplectic invariant near the focus–focus point, which is introduced by Vũ Ngọc. Examples of such calculations are still few. We compare our result with the semi-global symplectic invariant of the spherical pendulum.Open AccessSemi-Global Symplectic Invariant of the Champagne Bottle
We study a two degrees of freedom Hamiltonian system describing the motion of a particle in a potential field in the form of a symmetric double well, namely , known also as a champagne bottle potential. This system is completely integrable. The champagne bottle is the simplest member of a class of integrable systems that have no global action variables due to a non-trivial monodromy. Beyond that, the geometric and dynamical properties of the system near the equilibrium are of primary interest. We calculate the Birkhoff normal form and the nontrivial action near the focus–focus singularity and obtain the semi-global symplectic invariant near the focus–focus point, which is introduced by Vũ Ngọc. Examples of such calculations are still few. We compare our result with the semi-global symplectic invariant of the spherical pendulum. - 9 May 2025
- Published by Elsevier in Journal of Differential Equations
- Vol. 439
Dynamics of the Drinfeld-Sokolov-Wilson system: Well-posedness and (in)stability of the traveling waves
- 9 May 2025
- Published by Elsevier in Journal of Differential Equations
- Vol. 439
Dynamics of the Drinfeld-Sokolov-Wilson system: Well-posedness and (in)stability of the traveling waves
- Open Access
Dynamics of the Drinfeld-Sokolov-Wilson system: well-posedness and (in)stability of the traveling waves
We analyze the Drinfeld-Sokolob-Wilson system, which features a dispersive, KdV type evolution with a dispersionless conservation law. We establish well-posedness with low regularity initial data $L^2({\mathbb T})\times L^2({\mathbb T})$ for the Cauchy problem on periodic background, which is then extrapolated to global solutions, due to $L^2$ conservation law. We also establish a dynamically more relevant result, namely a global persistence of solutions with (large) initial data in $H^1({\mathbb T})\times L^2({\mathbb T})$. This is obtained by following a more sophisticated approach, specifically the method of normal forms. Finally, for a fixed period $L$, we construct an explicit one parameter family of periodic waves, see \eqref{2.16} below. We show that they are all spectrally unstable with respect to co-periodic perturbations. Specifically, we show that the Hamiltonian instability index is equal to one, which identifies the instability as a single positive growing mode.Open AccessDynamics of the Drinfeld-Sokolov-Wilson system: well-posedness and (in)stability of the traveling waves
We analyze the Drinfeld-Sokolob-Wilson system, which features a dispersive, KdV type evolution with a dispersionless conservation law. We establish well-posedness with low regularity initial data $L^2({\mathbb T})\times L^2({\mathbb T})$ for the Cauchy problem on periodic background, which is then extrapolated to global solutions, due to $L^2$ conservation law. We also establish a dynamically more relevant result, namely a global persistence of solutions with (large) initial data in $H^1({\mathbb T})\times L^2({\mathbb T})$. This is obtained by following a more sophisticated approach, specifically the method of normal forms. Finally, for a fixed period $L$, we construct an explicit one parameter family of periodic waves, see \eqref{2.16} below. We show that they are all spectrally unstable with respect to co-periodic perturbations. Specifically, we show that the Hamiltonian instability index is equal to one, which identifies the instability as a single positive growing mode. - 1 January 2023
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems-Series B
- Vol. 28 (8) , 4442-4456
On the integrability of twofold 1 : 2 Hamiltonian resonance
In a recent paper Mazrooei-Sebdani et al study a particular case of 1 : 2 : 1 : 2 Hamiltonian normal form, truncated to order 3. They find several cases of integrability. The main purpose of this work is to find other integrable cases. First, we obtain some integrable cases considering the known results about integrability the normal forms of 1 : 2 : 2 and 1 : 1 : 2 resonances. Then, we simplify this particular normal form, prove a non-integrability theorem and isolate a couple of non-trivial cases of integrability. These results can be applied, for example, in the study of normal forms of coupled elastic pendulums or coupled double pendulums, both in 1 : 2 resonance. On the other hand, it is definitely worth exploring the local and global properties of the geometry and the dynamics of all integrable cases, found here
- 1 January 2023
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems-Series B
- Vol. 28 (8) , 4442-4456
On the integrability of twofold 1 : 2 Hamiltonian resonance
In a recent paper Mazrooei-Sebdani et al study a particular case of 1 : 2 : 1 : 2 Hamiltonian normal form, truncated to order 3. They find several cases of integrability. The main purpose of this work is to find other integrable cases. First, we obtain some integrable cases considering the known results about integrability the normal forms of 1 : 2 : 2 and 1 : 1 : 2 resonances. Then, we simplify this particular normal form, prove a non-integrability theorem and isolate a couple of non-trivial cases of integrability. These results can be applied, for example, in the study of normal forms of coupled elastic pendulums or coupled double pendulums, both in 1 : 2 resonance. On the other hand, it is definitely worth exploring the local and global properties of the geometry and the dynamics of all integrable cases, found here
- Open Access
- 12 December 2022
- Published by Sofia University "St. Kliment Ohridski" in Annual of Sofia University St. Kliment Ohridski. Faculty of Mathematics and Informatics
- Vol. 109, 57-69
Non-integrability of a system from the rigid body dynamics
We study the complete integrability of a system describing the motion of a rigid body with a fixed point and a particle oscillating in it in the absence of external forces. Using the Ziglin-Morales-Ramis theory, we prove rigorously that the considered system is integrable only in the case of dynamical symmetry.
- 12 December 2022
- Published by Sofia University "St. Kliment Ohridski" in Annual of Sofia University St. Kliment Ohridski. Faculty of Mathematics and Informatics
- Vol. 109, 57-69
Open AccessNon-integrability of a system from the rigid body dynamics
We study the complete integrability of a system describing the motion of a rigid body with a fixed point and a particle oscillating in it in the absence of external forces. Using the Ziglin-Morales-Ramis theory, we prove rigorously that the considered system is integrable only in the case of dynamical symmetry.
- 15 October 2021
- Published by Springer Nature in The European Physical Journal Plus
- Vol. 136 (10) , 1-19
Non-integrability of a three-dimensional generalized Hénon-Heiles system
- 15 October 2021
- Published by Springer Nature in The European Physical Journal Plus
- Vol. 136 (10) , 1-19
Non-integrability of a three-dimensional generalized Hénon-Heiles system
- 2 November 2020
- Published by Springer Nature in Nonlinear Dynamics
- Vol. 102 (4) , 2295-2309
On the integrability of Hamiltonian 1:2:2 resonance
- 2 November 2020
- Published by Springer Nature in Nonlinear Dynamics
- Vol. 102 (4) , 2295-2309
On the integrability of Hamiltonian 1:2:2 resonance
- Open Access
Near-Integrability of Periodic Klein-Gordon Lattices
In this paper, we study the Klein-Gordon (KG) lattice with periodic boundary conditions. It is an N degrees of freedom Hamiltonian system with linear inter-site forces and nonlinear on-site potential, which here is taken to be of the form. First, we prove that the system in consideration is non-integrable in Liouville sense. The proof is based on the Morales-Ramis-Simó theory. Next, we deal with the resonant Birkhoff normal form of the KG Hamiltonian, truncated to order four. Due to the choice of potential, the periodic KG lattice shares the same set of discrete symmetries as the periodic Fermi-Pasta-Ulam (FPU) chain. Then we show that the above normal form is integrable. To do this we use the results of B. Rink on FPU chains. If N is odd this integrable normal form turns out to be KAM nondegenerate Hamiltonian. This implies that almost all low-energetic motions of the periodic KG lattice are quasi-periodic. We also prove that the KG lattice with Dirichlet boundary conditions (that is, with fixed endpoints) admits an integrable, nondegenerate normal forth order form. Then, the KAM theorem applies as above.Open AccessNear-Integrability of Periodic Klein-Gordon Lattices
In this paper, we study the Klein-Gordon (KG) lattice with periodic boundary conditions. It is an N degrees of freedom Hamiltonian system with linear inter-site forces and nonlinear on-site potential, which here is taken to be of the form. First, we prove that the system in consideration is non-integrable in Liouville sense. The proof is based on the Morales-Ramis-Simó theory. Next, we deal with the resonant Birkhoff normal form of the KG Hamiltonian, truncated to order four. Due to the choice of potential, the periodic KG lattice shares the same set of discrete symmetries as the periodic Fermi-Pasta-Ulam (FPU) chain. Then we show that the above normal form is integrable. To do this we use the results of B. Rink on FPU chains. If N is odd this integrable normal form turns out to be KAM nondegenerate Hamiltonian. This implies that almost all low-energetic motions of the periodic KG lattice are quasi-periodic. We also prove that the KG lattice with Dirichlet boundary conditions (that is, with fixed endpoints) admits an integrable, nondegenerate normal forth order form. Then, the KAM theorem applies as above. - Open Access
- 22 January 2018
- Published by Wiley in Advances in Mathematical Physics
- Vol. 2018, 1-12
Near-Integrability of Low-Dimensional Periodic Klein-Gordon Lattices
The low-dimensional periodic Klein-Gordon lattices are studied for integrability. We prove that the periodic lattice with two particles and certain nonlinear potential is nonintegrable. However, in the cases of up to six particles, we prove that their Birkhoff-Gustavson normal forms are integrable, which allows us to apply KAM theory in most cases.
- 22 January 2018
- Published by Wiley in Advances in Mathematical Physics
- Vol. 2018, 1-12
Open AccessNear-Integrability of Low-Dimensional Periodic Klein-Gordon Lattices
The low-dimensional periodic Klein-Gordon lattices are studied for integrability. We prove that the periodic lattice with two particles and certain nonlinear potential is nonintegrable. However, in the cases of up to six particles, we prove that their Birkhoff-Gustavson normal forms are integrable, which allows us to apply KAM theory in most cases.