Geometry of jet spaces and integrable systems
- Joseph Krasil'shchik, A. Verbovetsky
- Mathematics
- 30 January 2010
Homological Methods in Equations of Mathematical Physics
- Joseph Krasil'shchik, A. Verbovetsky
- Mathematics
- 31 August 1998
These lecture notes are a systematic and self-contained exposition of the cohomological theories naturally related to partial differential equations: the Vinogradov C-spectral sequence and the…
The Symbolic Computation of Integrability Structures for Partial Differential Equations
- Joseph Krasil'shchik, A. Verbovetsky, R. Vitolo
- MathematicsTexts & Monographs in Symbolic Computation
- 4 April 2018
We present a unified mathematical approach to the symbolic computation of integrability structures of partial differential equations, like Hamiltonian operators, recursion operators for symmetries…
On one-parametric families of Backlund transformations
- S. Igonin, Joseph Krasil'shchik
- Mathematics
- 25 October 2000
In the context of the cohomological deformation theory, infini- tesimal description of one-parametric families of Backlund transformations of special type including classical examples is given. It is…
Complete integrability of the coupled KdV-mKdV system
- P. Kersten, Joseph Krasil'shchik
- Mathematics, Physics
- 25 October 2000
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 recursion operator…
Secondary Calculus and Cohomological Physics
- M. Henneaux, Joseph Krasil'shchik, A. Vinogradov
- Physics
- 15 July 1998
Coverings and Integrability of the Gauss–Mainardi–Codazzi Equations
- Joseph Krasil'shchik, M. Marvan
- Mathematics
- 9 December 1998
Using the covering theory approach (zero-curvature representations with the gauge group SL), we insert the spectral parameter into the Gauss–Mainardi–Codazzi equations in Chebyshev and geodesic…
Computational Problems and Dedicated Software
- Joseph Krasil'shchik, A. Verbovetsky, R. Vitolo
- Mathematics
- 2017
In this chapter, we give an overview of the basic computational problems that arise in the study of geometrical aspects related to nonlinear partial differential equations and in the study of their…
EditorialNonlinear partial differential equations: Integrability, geometry and related topics
- Joseph Krasil'shchik, V. Rubtsov
- Mathematics
- 1 March 2017
Geometry of Differential Equations: A Concise Introduction
- Joseph Krasil'shchik
- Mathematics
- 1 June 2002
A short introduction to geometrical theory of nonlinear differential equations is given to provide a unified overview to the collection 'Symmetries of differential equations and related topics'.
...
...