3 papers
nlin.SI2000
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…
nlin.SI2000
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…
math.DG1998
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…