To 110-th Anniversary of N.G.Chebotarev

ALL-Russian school-conference

Chebotarev Conference on problems of modern group analysis

and applications to nonlinear mechanics

(Russia, Kazan, June, 2004)

A.N.Kusyumov

Kazan State Technical University of A.N.Tupolev's name

10, K.Marx str., Kazan, 420111, Russia

The All-Russian School-Conference on problems of the modern group analysis and its applications in the nonlinear mechanics was held in Kazan (June, 25-29, 2004). The Conference was organized and sponsored by Scientific-Research Institute of Mathematics and Mechanics of N.G.Chebotarev's name (SRIMM) and Kazan State Technical University of A.N.Tupolev's name (KSTU-KAI) on scientific direction, that has old, deep traditions in Kazan. This Conference was dedicated to 110-th Anniversary from birthday of N.G.Chebotarev, prominent mathematician, founder of SRIMM. The School-Conference was connected also with two scientific events, having the important significance for scientific community in whole, - 200-th Anniversary of Kazan State University (KSU) and 70-th Anniversary of SRIMM.

It is well known, the Russian School of the group analysis traditionally takes a leading position in the World. On development of this direction the strongest influence have rendered L.V.Ovsyannikov, N.H.Ibragimov. In Russia there are Scientific Centers, that are developing the traditions of the Russian School of the group analysis (Moscow, Novosibirsk, Krasnoyarsk, Ufa, St.-Petersburg etc.),. The representatives of these schools have taken part at the School-Conference for discussions about modern level and perspectives in group analysis area. Also important aim of Conference was the involving of youth energy to problems of this scientific area.

Main directions of development of the modern group analysis with the applications to differential equations:

-         research of equations of liquid and gas mechanics and other areas of a mechanics, with the purpose of accumulation of "database" equations, containing the exact analytical solution;

-         development of the classical group analysis with the applications to differential equations;

-         search of new directions of use of the group analysis for the applications to differential equations.

The first direction was presented by a lot of papers (V.K.Andreev, K.G.Garaev, S.I.Senashov, S.S.Titov, V.A.Chugunov etc.). In these papers the group analysis was used for constructing of the invariant solutions of equations set from different mechanic areas.

The second direction (development of the classical group analysis) is elaborating the algorithms, which were used earlier, but because of their difficulty the algorithms have no the completed or regular formalization. At a this school-conference second direction was presented, in particular, by S.V.Khabirov with Colleagues (constructing of differential-invariant submodels), A.N.Kusyumov, V.G.Pavlov (constructing of the invariant solutions without transition to factors-systems of differential equations).

The third direction includes the problems of elaboration of new algorithms permitting to expand the group analysis capabilities in the applications to differential equations systems which can not be analyzed by the classical group analysis. This direction was presented by Yu.N.Pavlovski (decomposition problem), M.B.Sheftel (using of partner symmetries for manifolds with the given metric structure of space).

The largest delegation of participants at this School-Conference was presented by scientific school of V.F.Zaitsev (St.-Petersburg). Main recent direction of activity of this school is the research of equivalence of the different forms of the non-local operators permitted by ordinary differential equations. The solution of inverse problems allows to choose the optimal form for this class of equations. The choosing of this form allows to perform the equations factorization by effective algorithm. In this case it is possible to find the solution for equations, which can not be solved by methods of the classical group analysis.

Many interesting plenary papers, surveys, problematic and original papers were presented at School-Conference, characterizing the modern level and trends in this interesting area of mathematics and mechanics.

 

 

Alexander N.Kusyumov, Dr., Kazan state technical university of A.N.Tupolev's name; scientific interests: geometry of partial differential equations and problems of the group analysis, constructions of conservation laws.