133 citations · 217 across the 5 of their papers we have counts for
5 papers
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…
Complete integrability of the coupled KdV-mKdV system
Paul Kersten, Joseph Krasil'shchik
The coupled KdV-mKdV system arises as the classical part of one of superextensions of the KdV equation. For this system, we prove its complete integrability, i.e., existence of a r…
On one-parametric families of Backlund transformations
Sergei Igonin, Joseph Krasil'shchik
In the context of the cohomological deformation theory, infinitesimal description of one-parametric families of Backlund transformations of special type including classical example…
Coverings and integrability of the Gauss-Mainardi-Codazzi equations
Joseph Krasil'shchik, Michal Marvan
Using covering theory approach (zero-curvature representations with the gauge group SL2), we insert the spectral parameter into the Gauss-Mainardi-Codazzi equations in Tchebycheff…
Homological Methods in Equations of Mathematical Physics
Joseph Krasil'shchik, Alexander Verbovetsky
These lecture notes are a systematic and self-contained exposition of the cohomological theories naturally related to partial differential equations: the Vinogradov C-spectral sequ…