Date of birth: February 10, 1948. E.mail: josephk @ diffiety.ac.ru
1966 - 1971: A student of the Moscow State University, Mechanical &
Mathematical Faculty.
1972 - 1980: Researcher at the All-Union Institute for Scientific and
Technology Information (USSR Academy of Sciences).
1981 - 1989: Senior researcher at the same Institute.
1989 - 1992: Senior lecturer at the Moscow Institute for Municipal
Economy and Civil Engineering.
1992 - 1999: Associate professor at the same Institute.
1999 - 2003: Full professor at the same Institute.
2004 - 2007: Full professor at the Moscow State Technical University of
Civil Aviation.
1997 up to now: Full professor at the
Independent University of Moscow 2007 up to now: Full professor at the
Russian State University for the Humanities 1991 - 1993: Scientific deputy director of the Moscow Sophus Lie
Center.
1978: Ph.D. degree in Information Science. 1997: Doctor of Science degree in Mathematics.
Current research: algebraic models and cohomological methods in PDE,
nonlocal structures, Poisson-Nijenhuis and Hamiltonian structures in PDE
A. Verbovetsky, V. Golovko, I. Krasil'shchik,
Variational Poisson-Nijenhuis structures for partial differential equations,
Theor. Math. Phys., 154 (2008) no. 2 (to appear).
I.S. Krasil'shchik, Natural coverings and integrable systems, In
Symmetries: Theoretical and Methidological Aspects, Astrakhan, 2007,
pp. 46-53 (in Russian).
I. Krasil'shchik, Nonlocal geometry of PDEs and integrability,
In: G. Gaeta, R. Vitolo, R. Walcher
(editors), Symmetry
and Pertubation Theory, World Scietific, 2007, pp. 100-108.
A. Verbovetsky, V. Golovko,
I. Krasil'shchik, Lie bracket for nonlocal shadows, Scientific
Bulletin of MSTUCA, 114 (2007) 4, 9-23 (in Russian).
P.H.M. Kersten, I.S. Krasil'shchik, The Cartan covering and
complete integrability of the KdV-mKdV system. In: Constructive Algebra and
Systems Theory, B. Hanzon and M. Hazewinkel (Editors) Royal Netherlands
Academy of Arts and Sciences, 2006.
P.H.M. Kersten,
I.S. Krasil'shchik,
and A.M. Verbovetsky, The Monge-Ampere
equation: Hamiltonian and symplectic structures, recursions, and
hierarchies.
Memorandum
1727, Faculty EEMCS University of Twente, 2004, 75 pp.
P.H.M. Kersten,
I.S. Krasil'shchik,
and A.M. Verbovetsky, On the
integrability conditions for some structures related to evolution
differential equations, Acta Appl. Math., 83 (2004) no. 1-2,
167-173.
arXiv:math.DG/0310451
S.A. Igonin,
P.H.M. Kersten, and I.S. Krasil'shchik, On symmetries and
cohomological invariants of equations possessing flat representations,
Memorandum 1639, Faculty of Mathematical Sciences University of Twente,
2002, 24 pp. J. of Diff. Geom. and Its Appl. 19 (2003) no. 3,
319-342. The Diffiety Inst. Preprint
Series, DIPS 7/2002. See
also:
arXiv:math.DG/0301344
P.H.M. Kersten, I.S. Krasil'shchik,
and A.M. Verbovetsky, An extensive
study of the N=1 supersymmetric KdV
equation,
Memorandum 1656, Faculty of Mathematical Sciences University of Twente,
2002, 63 pp.
I.S. Krasil'shchik, Geometry of differential equations: a
concise introduction, Acta Appl. Math., 72, (2002) no. 1-2,
1--17.
I.S. Krasil'shchik, A simple method to prove locality of
symmetry hierarchies, 4 pp. The Diffiety Inst. Preprint
Series, DIPS 9/2002.
I.S. Krasil'shchik, P.H.M. Kersten,
Complete integrability of the coupled KdV-mKdV system. In: T. Morimoto,
H. Sato, and K. Yamaguchi, eds.,
Lie Groups, Geometric Structures and Differential Equations - One
Hundred Years After Sophus Lie, Advanced Studies in Pure Mathematics,
vol.37, Math. Soc. of Japan, 2002,
151-171. arXiv:nlin.SI/0010041
I.S. Krasil'shchik, S. Igonin, On one-parametric families of
Baecklund transformations. In: T. Morimoto, H. Sato, and K. Yamaguchi,
eds., Lie Groups, Geometric Structures and Differential Equations - One
Hundred Years After Sophus Lie, Advanced Studies in Pure Mathematics,
vol.37, Math. Soc. of Japan, 2002,
99-114. arXiv:nlin.SI/0010040
I.S. Krasil'shchik, Integrability and supersymmetry. Proc. Conf.
Lie Groups, Geometric Structures and Differential Equations, Kyoto--Nara,
Japan, December 1999 (RIMS Lecture Notes, v. 1150 (2000). Kyoto,
Japan).
I.S. Krasil'shchik,, Deformations and integrable systems. Proc.
Conf. Differential Equations and Related Topics dedicated to 100th
Anniversary of birthday of I.G. Petrovskii, Moscow, Russia, 2001.
I.S. Krasil'shchik, On one-parametric families of Baecklund
transformations, The Diffiety Inst. Preprint
Series, DIPS 1/2000.
I.S. Krasil'shchik, P.H.M. Kersten,
Symmetries and Recursion Operators for Classical and Supersymmetric
Differential Equations, - Mathematics and its applications, Volume
507, Kluwer Acad. Publ., Dordrecht/Boston/London, 2000, 400 pp. For
more information see
here.
I.S. Krasil'shchik,
M. Marvan, Coverings and Integrability of the Gauss-Mainardi-Codazzi
Equations,
Acta Appl. Math.56, no. 2-3, 1999.
PS and
PDF-files
see on the ESI WWW-server.
See also arXiv:solv-int/9812010
I.S. Krasil'shchik. (in collaboration with B. Prinari), Lectures
on Linear Differential Operators over Commutative Algebras (The 1st
Italian Diffiety School, July, 1998). The Diffiety Inst. Preprint
Series, DIPS 1/99.
I.S. Krasil'shchik Cohomology background in geometry of PDE,
in M. Henneaux,
I. Krasil'shchik, and A.M. Vinogradov
(Eds.) Secondary Calculus and Cohomological Physics,
Contemporary Mathematics, vol.219, American Mathematical Society,
Providence, RI, 1998, pp. 121-139. See also The Diffiety Inst. Preprint
Series, DIPS 1/98.
I.S. Krasil'shchik Algebras with flat connections and symmetries
of differential equations, in Lie Groups and Lie Algebras: Their
Representations, Generalizations and Applications, Kluwer Acad. Publ.,
Dordrecht/Boston/London, 1998, pp. 407-424.
I.S. Krasil'shchik, Calculus over commutative algebras: a concise
user guide, Acta Appl. Math., Volume 49, Issue 3, December 1997,
pp. 235-248. See also The Diffiety Institute
Preprints, DIPS 1/96
I.S. Krasil'shchik, Characteristics of linear differential
operators over commutative algebras, Acta Appl. Math., Volume 49,
Issue 3, December 1997, pp. 257-269. See also The Diffiety Institute
Preprints, DIPS 2/96
I.S. Krasil'shchik, Poincare delta-lemma for smooth
algebras, Acta Appl. Math., Volume 49, Issue 3, December 1997,
pp. 249-255. See also The Diffiety Institute
Preprints, DIPS 3/96
I.S. Krasil'shchik, A supersymmetry approach to Poisson
structures over differential
equations, Proc. Conf. Diff. Geom. Appl., Brno, 1996, 14
pp. TeX-file see
on the EMIS WWW-server
I.S. Krasil'shchik, Poisson structures on nonlinear evolution
equations, Memorandum of the Twente University (1996), no. 1320, 24pp.
I.S. Krasil'shchik, Symmetries and recursion operators for soliton
equations, Proc. 1st Non-Orthodox School on Nonlinearity and Geometry, Warsaw
21 - 28 September 1995. Banach Center Publ, Warsaw, 1996.
I.S. Krasil'shchik, Hamiltonian formalism and supersymmetry for
nonlinear differential equations, Preprint of the Erwin Schroedinger
International Inst. for Mathematical Physics (1995), no. 257, Wien, 61
pp.
PS and
PDF-files
see on the ESI WWW-server.
I.S. Krasil'shchik, Notes on coverings and Baecklund
transformations, Preprint of the Erwin Schroedinger International
Inst. for Mathematical Physics (1995), no. 260, Wien, 15 pp.
PS and
PDF-files
see on the ESI WWW-server.
I.S. Krasil'shchik, P.H.M. Kersten,
Graded differential equations and their deformations: a computational
theory for recursion operators, Acta Appl. Math.41 (1995)
167 - 191. Also in:
P.H.M. Kersten and I.S. Krasil'shchik (eds.) Geometric and
Algebraic Structures in Differential Equations, Kluwer Acad. Publ.,
Dordrecht/Boston/London, 1995.
I.S. Krasil'shchik, P.H.M. Kersten,
Deformations and recursion operators for evolution equations, Memorandum of
the Twente University (1992), no. 1104, Enschede, 47 pp. Also in: Prastaro,
A. and Rassias, Th.M. (eds.), Geometry in partial differential
equations, World Scientific, Singapore, 1994.
I.S. Krasil'shchik, Lie algebra structures for the symmetries of
differential equations possessing recursion operators, Preprint of the
Erwin Schroedinger International Inst. for Mathematical Physics (1993),
no. 47, Wien, 14 pp.
PS and
PDF-files
see on the ESI WWW-server.
I.S. Krasil'shchik, An algebraic model for characteristics of
differential equations Preprint of the Erwin Schroedinger International
Inst. for Mathematical Physics (1993), no. 48, Wien, 14 pp.
PS and
PDF-files
see on the ESI WWW-server.
I.S. Krasil'shchik, Deformation algebras of differential
equations and recursion operators, Transactions of the Sci. Conf. of
MIMECI, Moscow Inst. for Municipal Economy and Civil Engineering, Moscow,
1992 (in Russian).
I.S. Krasil'shchik, Schouten
brackets and canonical algebras - Global Anal. and
Math. Physics, Voronezh State University, 1987 (in Russian, English
translation in: Springer Lecture Notes in Math. 1334,
Springer-Verlag, 1988).
I.S. Krasil'shchik, Why Baecklund transformation form a group?
(1987), Mimeographed notes (in Russian).
I.S. Krasil'shchik,
V.V. Lychagin,
A.M. Vinogradov,
Introduction into the Geometry of Nonlinear Differential Equations,
Nauka Publ. House, Moscow, 1986 (in Russian).
I.S. Krasil'shchik,
V.V. Lychagin, A.M. Vinogradov,
Geometry of Jet Spaces and Nonlinear Differential Equations, Gordon
and Breach Sci. Publ., New York, 1986.
I.S. Krasil'shchik, Poincare delta - lemma, Proc. of the
Seminar on Algebra and Geometry of Differential Equations, Moscow
State University, Moscow, 1986 (in Russian).
I.S. Krasil'shchik,
V.V. Lychagin,
A.M. Vinogradov,
Applications of nonlinear differential equations in civil aviation,
Moscow Institute of Civil Aviation Engineers, Moscow, 1977 (in Russian).
I.S. Krasil'shchik, Hamiltonian formalism in canonical rings, The
8th Winter Mathematical School, Voronezh State University, Voronezh, 1974
(in Russian).