66 citations
- National Research University Higher School of EconomicsRU13 papers
- Lomonosov Moscow State UniversityRU12 papers
- Landau Institute for Theoretical PhysicsRU8 papers
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- P.N. Lebedev Physical Institute of the Russian Academy of SciencesRU5 papers
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5 papers · 1 filter
On integrability of the Camassa-Holm equation and its invariants. A geometrical approach
Valentina Golovko, Paul Kersten, Iosif Krasil'shchik +1
Using geometrical approach exposed in arXiv:math/0304245 and arXiv:nlin/0511012, we explore the Camassa-Holm equation (both in its initial scalar form, and in the form of 2x2-syste…
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…
Derived categories of Fano threefolds
Alexander Kuznetsov
We consider the structure of the derived categories of coherent sheaves on Fano threefolds with Picard number 1 and describe a strange relation between derived categories of differ…
Regular subalgebras of affine Kac-Moody algebras
Anna Felikson, Alexander Retakh, Pavel Tumarkin
We classify regular subalgebras of affine Kac-Moody algebras in terms of their root systems. In the process, we establish that a root system of a subalgebra is always an intersecti…