19 citations · 43 across the 5 of their papers we have counts for
5 papers
On integrable structures for a generalized Monge-Ampere equation
Paul Kersten, Iosif Krasil'shchik, Alexander Verbovetsky +1
We consider a 3rd-order generalized Monge-Ampere equation u_yyy - u_xxy^2 + u_xxx u_xyy = 0 (which is closely related to the associativity equation in the 2-d topological field the…
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…
Integrability of Kupershmidt deformations
Paul Kersten, Iosif Krasil'shchik, Alexander Verbovetsky +1
We prove that the Kupershmidt deformation of a bi-Hamiltonian system is itself bi-Hamiltonian. Moreover, Magri hierarchies of the initial system give rise to Magri hierarchies of K…
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…
On symmetries and cohomological invariants of equations possessing flat representations
S. Igonin, P. H. M. Kersten, I. Krasil'shchik
We study the equation E_fc of flat connections in a fiber bundle and discover a specific geometric structure on it, which we call a flat representation. We generalize this notion t…