74 citations · 309 across the 33 of their papers we have counts for
7 papers · 1 filter
On variational bivectors
I. S. Krasil'shchik
We construct examples of variational bivectors that are not Poissonian.
Hamiltonian structures for general PDEs
Paul Kersten, Iosif Krasil'shchik, Alexander Verbovetsky +1
We sketch out a new geometric framework to construct Hamiltonian operators for generic, non-evolutionary partial differential equations. Examples on how the formalism works are pro…
Variational Poisson-Nijenhuis structures for partial differential equations
Valentina Golovko, Iosif Krasil'shchik, Alexander Verbovetsky
We explore variational Poisson-Nijenhuis structures on nonlinear PDEs and establish relations between Schouten and Nijenhuis brackets on the initial equation with the Lie bracket o…
Algebraic theories of brackets and related (co)homologies
Iosif Krasil'shchik
A general theory of the Frolicher-Nijenhuis and Schouten-Nijenhuis brackets in the category of modules over a commutative algebra is described. Some related structures and (co)homo…
On the integrability conditions for some structures related to evolution differential equations
Paul Kersten, Iosif Krasil'shchik, Alexander Verbovetsky
Using the result by D.Gessler (Differential Geom. Appl. 7 (1997) 303-324, DIPS-9/98, http://diffiety.ac.ru/preprint/98/09_98abs.htm), we show that any invariant variational bivecto…
Hamiltonian operators and l*-coverings
Paul Kersten, Iosif Krasil'shchik, Alexander Verbovetsky
An efficient method to construct Hamiltonian structures for nonlinear evolution equations is described. It is based on the notions of variational Schouten bracket and l*-covering.…