# Ognyan Borisov Christov

Associate professor
DSc

### Differential Equations

Email:
christov@fmi.uni-sofia.bg
Phone:
+359 2 8161-519
Room:
Faculty of Physics, 26
Office hours:

Thursday 12-15

### Publications

1. Stability of the equilibrium positions of a Satellite - Gyrostate system with a dempfer, J. Theor.  Appl. Mech, 1,1990, 19 - 29.   (with L. Lilov) (in Russian).
2. On planar oscillations of gyrostat on elliptic orbit, J. Theor.  Appl. Mech., 2, 1991, 22 - 28.
3. Perturbations of a mechanical system with two degrees of freeedom J. Theor.  Appl. Mech., 3, 1992, 36 - 49.
4. Stability of certain solutions in a mechanical model generating the rigid body problem, J. Theor.  Appl. Mech. , 4, 1993, 9 - 21.
5. Bifurcations of invariant manifolds in a model in rigid body dynamics, Ann. de L' Univ. de Sofia, L. 2 - Mech., 85, 1991, 123 -129.
6. On a perturbations of a mechanical system from rigid body dynamics, Ann. de L' Univ. de Sofia, L. 2, 86, 1992, 5 - 15.
7. On the stability of Lyapunov's periodic solutions of a mechanical system with  two degrees of freedom, J. Theor.  Appl. Mechanics, 2,  1993, 27 - 32.
8. On the non-integrability of a system describing the motion of a rigid body with a fixed point and a particle oscillating in it, C. R. Acad. Bul. Sci., 46, (1993), no. 9, p. 33-36.
9. On the Kolmogorov's condition for the Kirchhoff top, C. R. Acad. Bul. Sci., 47, (1994), no. 6, p. 17-20.
10. On the Kolmogorov's condition for the special case of the Kirchhoff top, J. Math. Phys., 35(7), 3448 - 3463, 1994.
11. On the non-integrability of a system describing the motion of a rigid body with a fixed point and a particle oscillating in it, Bull. Sci. Math., 118,4, 385-401, 1994.
12. Perturbations of systems describing the motion of a particle in central fields, Serdica Math. J.,21, 1995, 91-108. (with D. Dragnev)
13. On the chaotic behaviour of a system from the rigid body dynamics, J. Theor.  Appl. Mech., No. 3, 1996, 9 - 16.
14. A note on instability of spatially quasi - periodic states of the Ginzburg - Landau equation, Phys. Lett. A 228 (1997), 53 - 58.
15. On the KAM - theory conditions for the Kirchhoff top, Serdica Math. J., 23, 1997, 113-124.
16. Effective solutions of Clebsch and C. Neumann systems, Sitzungsberichte der Berliner Mathematische Gesellschaft, 1997 - 2000, 217 - 242. (with A. Zhivkov)
17. Remark on the non-integrability of the perturbed motion in a central field in constant curvature spaces, Ann. de L' Univ. de Sofia, t. 93, 1999, 25-30.
18. Неинтегруемост на Хамилтонови системи и диференциална теория на Галоа, Доклади на пролетната конференция на българските математици, Боровец, 2002, 58-65.
19. Non-integrability of the second Painleve equation as a Hamiltonian system, Comp. Rend. Acad. Bulg. Sci. 60, 1, (2007), 13-18. (with T. Stoyanova)
20. Non-integrability of a Hamiltonian system, based on a problem of nonlinear vibration of  an elastic string, Ann. Univ. Sofia, Fac. Math. Inf, 99, 2008, 91-107. (with P. Braynova)
21. On the inverse scattering approach and action-angle variables for the Dullin-Gottwald-Holm equation, Phys. D 238 (2009), 9 - 19. (with S. Hakkaev)
22. On the number of spikes of  solutions for a singularly perturbed boundary value problem, NAA'2008, S. Margenov et all (Eds.), LNCS 5434, Springer, 2009, pp. 233-240.
23. On the Cauchy problem for the periodic b-family of equations and of the non-uniform continuity of Degasperis-Procesi equation, J. Math. Anal. Appl. 360 (2009), 47-56. (with S. Hakkaev)
24. Near Integrability in Low dimensional Gross-Neveu Models, Z. Naturforsch.  66a (2011), 468-480.
25. Geometric Integrability of Some Generalizations of the Camassa-Holm Equation, International J. of Diff. Equ., Vol. 2011, ID738509, 13pp, 2011.
26. Non-integrability of first order resonances in Hamiltonian systems in three degrees of freedom, Celest. Mech. Dyn. Astr. 112 (2012), 149-167.
27. Non-uniform continuity of periodic Holm-Staley b-family of equations, Nonlinear Analysis TMA,  75 (2012) 4821-4838. (with S. Hakkaev and I. Iliev)
28. On the nonlocal symmetries of the $\mu$-Camassa-Holm equation, J. Nonl. Math. Phys., 19, No.3 1250025 (17pp),  (2012).
29. Canonically conjugate variables for the $\mu$CH equation, Pliska Stud. Math. Bulg., 21 (2012) 287-298.
30. On the integrability of a system describing the stationary solutions in Bose-Fermi mixtures, Chaos, Solitons and Fractals, 77 (2015), pp. 138-148 (with G. Georgiev).
31. Non-Integrability of Some Higher-Order Painleve Equations in the sense of Liuville, SIGMA, 11 (2015) 045, 20pp. (with G. Georgiev).
32. Non-integrability of the Karabut system, Nonlinear Analysis: Real World Applications, 32 (2016) 91-97.