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UNIVERZA V MARIBORU $\bullet$ UNIVERSITY OF MARIBOR
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PROF.DR. MARKO ROBNIK, DIRECTOR

Seminarsko predavanje
Centra za uporabno matematiko in teoretično fiziko

On Some Approach to Construction of the Higher Order Painlevé Equations

Professor Dr. Valeri I. Gromak
Faculty of Mechanics and Mathematics, Belarusian State University Minsk, Belarus

Abstract: We consider the hierarchies of Painlevé type nonlinear ordinary differential equations (ODEs) that are generalizations of the Painlevé equations. These hierarchies arise as self - similar reductions of PDEs hierarchies or as equations of isomonodromic deformation of linear systems. The Painlevé equations can be regarded as completely integrable equations and possess hierarchies of algebraic solutions and one-parameter families of solutions expressible in terms of the classical special functions, for special values of the parameters. Further the Painlevé equations admit symmetries under affine Weyl groups. In the general case the Painlevé transcendent may be thought of as a nonlinear analogues of the classical special functions. Although first discovered from strictly mathematical considerations, the Painlevé equations have arisen in a variety of important physical applications.

Seminarsko predavanje bo v petek 19. julija 2013 ob 14:15 uri v seminarski sobi CAMTP, Krekova 2, pritličje desno. Vljudno vabljeni vsi zainteresirani, tudi študentje.

Prof.Dr. Marko Robnik
-- Direktor CAMTP --