The calculus of local variational differential operators introduced by B. L. Voronov, I. V. Tyutin, and Sh. S. Shakhverdiev is studied in the context of jet super space geometry. In a coordinate-freeâ€¦ (More)

Sergei Igonin, Joseph Krasilshchik, Joseph Krasilâ€²shchik, JOSEPH KRASILSHCHIK

2000

In the context of the cohomological deformation theory, infinitesimal description of one-parametric families of BÃ¤cklund transformations of special type including classical examples is given. It isâ€¦ (More)

Sergei IGONIN â€ , Alexander VERBOVETSKY â€¡ and Raffaele VITOLO Â§ â€ Department of Mathematics, Utrecht University, P.O. Box 80010, 3508 TA Utrecht, The Netherlands E-mail: igonin@mccme.ru â€¡ Independentâ€¦ (More)

We study the equation Efc of flat connections in a given fiber bundle and discover a specific geometric structure on it, which we call a flat representation. We generalize this notion to arbitraryâ€¦ (More)

We consider multidimensional systems of PDEs of generalized evolution form with t-derivatives of arbitrary order on the left-hand side and with the right-hand side dependent on lower orderâ€¦ (More)

Following I. S. Krasilshchik and A. M. Vinogradov [8], we regard PDEs as infinite-dimensional manifolds with involutive distributions and consider their special morphisms called differentialâ€¦ (More)

The Wahlquist-Estabrook prolongation method allows to obtain for some PDEs a Lie algebra that is responsible for Lax pairs and BÃ¤cklund transformations of certain type. We study theâ€¦ (More)

Following A.M. Vinogradov and I.S. Krasilshchik, we regard systems of PDEs as manifolds with integrable distributions and consider their special morphisms called differential coverings, which includeâ€¦ (More)

Let P be a parabolic subgroup of a semisimple complex Lie group G defined by a subset Î£ of simple roots of G, and let EÏ† be a homogeneous vector bundle over the flag manifold G/P corresponding to aâ€¦ (More)