5 citations · 9 across the 10 of their papers we have counts for
11 papers
A note on the integrability status of a 'mysterious' case of a quadratic Hamiltonian
Ognyan Christov
We present a simple algebraic proof of meromorphic non-integrability of a 'mysterious' case of a quadratic Hamiltonian studied by Sokolov and Wolf. The result is obtained by applyi…
Semi-global symplectic invariant of the champagne bottle
Ognyan Christov
We study a two degrees of freedom Hamiltonian system describing the motion of a particle in a potential field of the form of symmetric double well, namely $V = - (x_1^2 + x_2…
Dynamics of the Drinfeld-Sokolov-Wilson system: well-posedness and (in)stability of the traveling waves
Ognyan Christov, Sevdzhan Hakkaev, Seungly Oh +1
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 regulari…
Non-integrability of a three dimensional generalized Hénon-Heiles system
Ognyan Christov
In recent paper Fakkousy et al. show that the 3D Hénon-Heiles system with Hamiltonian $ H = \frac{1}{2} (p_1 ^2 + p_2 ^2 + p_3 ^2) +\frac{1}{2} (A q_1 ^2 + C q_2 ^2 + B q_3 ^2) + (…
Near-integrability of periodic Klein-Gordon lattices
Ognyan Christov
In this paper we study the Klein-Gordon (KG) lattice with periodic boundary conditions. It is an degrees of freedom Hamiltonian system with linear inter-site forces and nonline…
A note on the integrability of Hamiltonian 1 : 2 : 2 resonance
Ognyan Christov
We study the integrability of the Hamiltonian normal form of 1 : 2 : 2 resonance. It is known that this normal form truncated to order three is integrable. The truncated to order f…
Near-integrability of low dimensional periodic Klein-Gordon lattices
Ognyan Christov
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 non integ…
On the integrability of a system describing the stationary solutions in Bose--Fermi mixtures
Ognyan Christov, Georgi Georgiev
We study the integrability of a Hamiltonian system describing the stationary solutions in Bose--Fermi mixtures in one dimensional optical lattices. We prove that the system is inte…
Non-Integrability of Some Higher-Order Painlevé Equations in the Sense of Liouville
Ognyan Christov, Georgi Georgiev
In this paper we study the equation which is one of the higher-order Painlevé equations (i.e., equations in the…
Non-integrability of the second Painleve equation as a Hamiltonian system
Tsvetana Stoyanova, Ognyan Christov
We prove non-existence of an additional rational integral for the second Painleve equation considered as a Hamiltonian system using Morales - Ramis theory.
Non-uniform continuity of periodic Holm-Staley b-family of equations
Ognyan Christov, Sevdzhan Hakkaev, Iliya D. Iliev
We consider a family of non-evolutionary partial differential equations known as Holm - Staley b - family which includes the integrable Camassa-Holm and Degasperis-Procesi equation…