Department of Mathematics and InformaticsSofia University, 5 J. Bourchier Blvd.Sofia 1126, Bulgaria
Department of Mathematics and Informatics,Sofia University
Horozov E., Stoyanova C.
Non-Integrability of Some Painlevé VI-Equations and Dilogarithms
2007, vol. 12, no. 6, pp. 622-629
The paper studies the Painlevé VIe equations from the point of view of Hamiltonian nonintegrability. For certain infinite number of points in the parameter space we prove that the equations are not integrable. Our approach uses recent advance in Hamiltonian integrability reducing the problem to higher differential Galois groups as well as the monodromy of dilogarithic functions.
The Weyl Algebra, Bispectral Operators and Dynamics of Poles
2002, vol. 7, no. 4, pp. 399-424
The present paper reviews some new results in the study of the bispectral problem. We describe all bispectral operators in the Weyl algebra and the Darboux transformations of them. The dynamics of their poles is shown to be connected with the KP-hierarchy. The exposition is intended for readers with some experience in the subject. On the other hand being self-contained it can be used for a first acquaintance with the subject of bispectral operators.