The main scientific interests are related to the theoretical astrophysics, nonlinear physics and mainly to relativistic astrophysics. Being student and graduate trainee of acad. Ya. B. Zeldovich I had worked in the field of the physics of compact objects. My works are mainly oriented toward high-energy astrophysics, X - and Gamma - ray astronomy. My PhD thesis on "Non-stationary Disc Accretion" initiated a series theoretical works for group analysis of solution of equation describing accretion discs. The results obtained showed that the discs are ideal synergetic system with nonlinearity, irreversibility and openness. That is why together with acad. Ya.Zeldovich we explored the idea that the majority of dynamic manifestation of objects where accretion fluxes are observed or assumed, should be systemized and interpreted based on the theory of the self organisation. The investigation applies two parallel methods - the synergetic via obtaining wide class of analytical solutions and criteria to demonstrate under what conditions these objects express a distinct tendency toward self - organisation. This is rather euristic approach. The second approach is related to the investigation of the dynamic instability of the accretion fluxes. The instability of hydrodynamic and magnetohydrodynamic Quette flows may give the answer to one of the crucial questions in the theory of the disc accretion - the problem of the natural turbolization. The self gravitational and non self - gravitational instability of primordial accretion, solar and planetary dust layers in quasi - Keplerian differential rotation around a central gravitational field was theoretically investigated. For this purpose linear and non-linear perturbation analyses were applied to the full system of hydro-dynamical equations of the Eulerian type. Bending wave modes and compression waves were studied separately both for radial and tangential propagation directions. For radial waves a similar instability criterion like that by Goldreich and Ward was obtained. However, for tangential waves a different criterion was found clearly showing that the onset of the instability sensitively depends on the direction of propagation. This work is now successfully extended to the case of viscous accretion discs. Recently I have been working on the non-linear physics of accretion discs. The expected effects in such systems are as follows (to mention a few):

1. Shock waves may occur as a result of inflowing or outflowing nonstationary flux.

2. Self-organisations may be obtained as result of feed-back between accreting substance emissivity flux from the inner edge of the disc on the equatorial plane.

3. Defined current structures may occur from Rossby type solutions.

4. The appearance of most various types of instabilities which modulate the observational manifestation of these phenomena.

In addition, many other effects which influence the dynamics of the accretion flux could also be investigated. The developing phenomena would be different depending on whether the accretion disc is in the active galaxy nucleus, around black hole, neutron star, white dwarf or a protostar.. Therefore I have the idea to unify these phenomena and look for the guiding parameters in these systems in order to establish good classification.

Another problem I am interested in is the turbulence mechanism resulting from the evolution of a non-linear system. A non-linear theory of the hydrodynamical instability does not exist yet. Therefore I decided to apply the idea to describe non-linear parabolic equation as a revealing method for initial generation of pulsations with finite amplitude in accretion discs. For more than 10 years I have worked on the application of the ideas of synergetics and non-linear physics in astrophysics. Recently I have concentrated my research efforts on the problem of self-organisation of open and non-equilibrium systems which in fact are widely found in astrophysics. In mathematical terms, if in an open and non-equilibrium system there is transfer and a source of energy exists (either of internal or external nature) then a self-consistent structure formation should be initiated and the opposite, if this self - consistency is broken up then the system evolves again until a self - consistency is established once again. The problem is which are the guiding parameters characterising this evolutionary phase sequence of "structure - transition - structure" for various astrophysical objects. It is clear that for the systems with a gravitating centre in the sense of a star, the phases will undergo the following evolutionary process "authowave process -quasi-stationary state - autho-wave process - ...". For the systems without such a gravitation centre the phases should be "chaos -structure - chaos - …" and of course, one intermediate phase may exit. Then the turbulence interacts with the autho-wave processes and the whole processes can assume a more complicated but a more physical meaning. Such is the case with accretion discs, proto-planetary systems and galactic discs. One of the problems which motivated these studies is the cause for the development of turbulent motions in such rotating systems. The idea is that

THIS PHENOMENON HAS BEEN CAUSED BY THE FACT THAT SUCH AN OPEN AND NON-EQUILIBRIUM SYSTEM WITH DIFFERENTIAL

ROTATION CAN NOT RESIST GRAVITY IN NO OTHER WAY BUT BY DEVELOPING SUCH CHAOTIC MOTION.

Therefore the question what methods of the self - organisation theory can be applied in support of such a hypotheses emerges. The unification of the synergetics and the theory of dynamics instability will provide for the development of non-linear astrophysics, the premises of which we may find in the non-linear theory of star pulsations, jet and galactic dynamics. The development of the non-linear astrophysics would give the possibility many of the observed phenomena to be identified and classified and on the other hand new phenomena and physical manifestation would revealed whose existence might not be found employing the classical linear approach. An important role in the rapid solution of

these problems wouldbe the combination of theoretical and numerical experiment on one hand, and the comparison of the results obtained with theplethora of data from the specialised space and ground-based observations, on the other. Many of these problems are reflected in publications, others are projects of future work. Another field of scientific interest is the investigation of hot rarefied plasma in astrophysics. This problem was recently identified with respect to the investigations and the diagnostics of such plasma type around collapsed objects and on Sun. The future plans concern an extensive study on the problem of astrophysical radiation hydrodynamics and the eventual combination with the problems of the non-linear astrophysics. In this regard there is collaboration with Prof. G. Nikolis from the Brussels Free University on the "Non-linear evolution of accretion discs".