133 citations · 393 across the 12 of their papers we have counts for
12 papers
A unified approach to computation of integrable structures
Iosif Krasil'shchik, Alexander Verbovetsky, Raffaele Vitolo
We expose (without proofs) a unified computational approach to integrable structures (including recursion, Hamiltonian, and symplectic operators) based on geometrical theory of par…
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…
Geometry of jet spaces and integrable systems
Joseph Krasil'shchik, Alexander Verbovetsky
An overview of some recent results on the geometry of partial differential equations in application to integrable systems is given. Lagrangian and Hamiltonian formalism both in 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…
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…