Иосиф Красильщик - Academia.edu (original) (raw)

Papers by Иосиф Красильщик

Contemporary mathematics, 1998

Unstable bundles in quantum field theory by M. Asorey, F. Falceto, and G. Luzon Brackets in the j... more Unstable bundles in quantum field theory by M. Asorey, F. Falceto, and G. Luzon Brackets in the jet-bundle approach to field theory by G. Barnich The BRST structure of twisted N=2N = 2N=2 algebra by C. Becchi, S. Giusto, and C. Imbimbo Anomalies and locality in field theories and M-theory by L. Bonora, C. S. Chu, and M. Rinaldi Gauge covariant algebras and local BRST cohomology by F. Brandt Generalized homologies for dN=0d^N = 0dN=0 and graded qqq-differential algebras by M. Dubois-Violette Nonlinear control and diffieties, with an application to physics by M. Fliess, J. Levine, P. Martin, and P. Rouchon Consistent interactions between gauge fields: the cohomological approach by M. Henneaux A compatible analytic manifold structure for Lie pseudogroups of infinite type by N. Kamran and T. Robart Cohomology background in geometry of PDE by J. Krasilshchik Algebraic renormalization of massive supersymmetric theories by N. Maggiore A new look at completely integrable systems and double Lie groups by G. Marmo and A. Ibort Quantum dynamics of 3-D vortices by V. Penna, M. Rasetti, and M. Spera The (secret?) homological algebra of the Batalin-Vilkovisky approach by J. D. Stasheff Notes on the horizontal cohomology by A. Verbovetsky Invariants of rational transformations and algebraic entropy by C. M. Viallet Introdution to secondary calculus by A. Vinogradov On multiple generalizations of Lie algebras and Poisson manifolds by A. Vinogradov and M. Vinogradov.

Journal of Geometry and Physics, Mar 1, 2017

arXiv (Cornell University), Dec 9, 1998

Using covering theory approach (zero-curvature representations with the gauge group SL 2), we ins... more Using covering theory approach (zero-curvature representations with the gauge group SL 2), we insert the spectral parameter into the Gauss-Mainardi-Codazzi equations in Tchebycheff and geodesic coordinates. For each choice, four integrable systems are obtained.

Contemporary mathematics, 1998

arXiv (Cornell University), Oct 25, 2000

In the context of the cohomological deformation theory, infinitesimal description of one-parametr... more In the context of the cohomological deformation theory, infinitesimal description of one-parametric families of Bäcklund transformations of special type including classical examples is given. It is shown that any family of such a kind evolves in the direction of a nonlocal symmetry shadow in the sense of [10].

arXiv (Cornell University), Jan 3, 2014

In the framework of the theory of differential coverings [2], we discuss a general geometric cons... more In the framework of the theory of differential coverings [2], we discuss a general geometric construction that serves the base for the so-called Lax pairs containing differentiation with respect to the spectral parameter [4]. Such kind of objects arise, for example, when studying integrability properties of equations like the Gibbons-Tsarev one [1]. 2010 Mathematics Subject Classification. 37K10. Key words and phrases. Geometry of PDEs, differential coverings. I am grateful to the Mathematical Institute of the Silesian University in Opava for support and comfortable working condition.

arXiv (Cornell University), Aug 31, 1998

Proposition 1.2. Let P, Q and R be A-modules. Then: (1) If ∆ 1 ∈ Diff k (P, Q) and ∆ 2 ∈ Diff l (... more Proposition 1.2. Let P, Q and R be A-modules. Then: (1) If ∆ 1 ∈ Diff k (P, Q) and ∆ 2 ∈ Diff l (Q, R) are two differential operators, then their composition ∆ 2 • ∆ 1 lies in Diff k+l (P, R). (2) The maps i •,+ : Diff k (P, Q) → Diff + k (P, Q), i +,• : Diff + k (P, Q) → Diff k (P, Q) generated by the identical map of Hom k (P, Q) are differential operators of order ≤ k.

Texts and monographs in symbolic computation, 2017

Texts and monographs in symbolic computation, 2017

Texts and monographs in symbolic computation, 2017

Texts and monographs in symbolic computation, 2017

Texts and monographs in symbolic computation, 2017

The tangent covering is an equation naturally related to the initial equation \(\mathbb {E}\) and... more The tangent covering is an equation naturally related to the initial equation \(\mathbb {E}\) and which covers the latter and plays the same role in the category of differential equations that the tangent bundle plays in the category of smooth manifolds. It is used to construct recursion operators for symmetries of \(\mathbb {E}\) and symplectic structures on \(\mathbb {E}\). In this chapter we give the solution to Problem 1.18 and also prepare a basis to solution of Problems 1.20 (Chap. 7) and 1.22 (Chap. 8).

Texts and monographs in symbolic computation, 2017

A variational Poisson structure on a differential equation \(\mathcal {E}\) is a \(\mathcal {C}\)... more A variational Poisson structure on a differential equation \(\mathcal {E}\) is a \(\mathcal {C}\)-differential operator that takes cosymmetries of \(\mathcal {E}\) to its symmetries and possesses the necessary integrability properties. In the literature on integrable systems, Poisson structures are traditionally called Hamiltonian operators. We expose here the computational theory of local variational Poisson structures for normal equations. In this chapter the solutions of Problems 1.24, 1.25, 1.26, and 1.28 is presented.

This is an overview of recent results obtained by S. Igonin, P. Kersten, and A. Verbovetsky in co... more This is an overview of recent results obtained by S. Igonin, P. Kersten, and A. Verbovetsky in collaboration with the author and related to using of nonlocal constructions in geometry of partial di®erential equations. For general references concerning geometry of PDE see [1, 7]. Let E J1() 1¡¡! M be an in¯nitely prolonged di®erential equation con-sidered as a submanifold in an appropriate manifold of in¯nite jets. Then E is endowed with a natural ¯nite-dimensional integrable distribution (the Cartan dis-tribution denoted by C) locally spanned by the total derivatives. A ¯ber bundle ¿ : ~E! E is called a covering over E if (a) ~E is endowed with an integrable distri-bution ~C, dim ~C = dim C and (b) ¿ ¤ ~Cy = C¿(y) for any y 2 ~E. A 1 ± ¿-vertical vector ¯eld X is called a nonlocal symmetry of E if it preserves ~C. Nonlocal symmetries can be expressed in ¯nite terms rather rarely. A good (and rather useful) substitute is the notion of a shadow (that is often mixed up with nonlocal sy...

Astrakhan. In: Symmetries: Theoretical and Methidological Aspects, Astrakhan, 2007, pp. 46–53.

Encyclopedia of Complexity and Systems Science, 2009

arXiv: Exactly Solvable and Integrable Systems, 2020

We construct a three-component system of PDEs describing dynamics of van der Walls gas in one-dim... more We construct a three-component system of PDEs describing dynamics of van der Walls gas in one-dimensional nozzle. The group of conservation laws for this system is described. We also ompute the Lie algebras of point symmetries and present group classification. Exact invariant solutions are discussed.

一般社団法人電子情報通信学会, Jul 3, 2008

Contemporary mathematics, 1998

Unstable bundles in quantum field theory by M. Asorey, F. Falceto, and G. Luzon Brackets in the j... more Unstable bundles in quantum field theory by M. Asorey, F. Falceto, and G. Luzon Brackets in the jet-bundle approach to field theory by G. Barnich The BRST structure of twisted N=2N = 2N=2 algebra by C. Becchi, S. Giusto, and C. Imbimbo Anomalies and locality in field theories and M-theory by L. Bonora, C. S. Chu, and M. Rinaldi Gauge covariant algebras and local BRST cohomology by F. Brandt Generalized homologies for dN=0d^N = 0dN=0 and graded qqq-differential algebras by M. Dubois-Violette Nonlinear control and diffieties, with an application to physics by M. Fliess, J. Levine, P. Martin, and P. Rouchon Consistent interactions between gauge fields: the cohomological approach by M. Henneaux A compatible analytic manifold structure for Lie pseudogroups of infinite type by N. Kamran and T. Robart Cohomology background in geometry of PDE by J. Krasilshchik Algebraic renormalization of massive supersymmetric theories by N. Maggiore A new look at completely integrable systems and double Lie groups by G. Marmo and A. Ibort Quantum dynamics of 3-D vortices by V. Penna, M. Rasetti, and M. Spera The (secret?) homological algebra of the Batalin-Vilkovisky approach by J. D. Stasheff Notes on the horizontal cohomology by A. Verbovetsky Invariants of rational transformations and algebraic entropy by C. M. Viallet Introdution to secondary calculus by A. Vinogradov On multiple generalizations of Lie algebras and Poisson manifolds by A. Vinogradov and M. Vinogradov.

Journal of Geometry and Physics, Mar 1, 2017

arXiv (Cornell University), Dec 9, 1998

Using covering theory approach (zero-curvature representations with the gauge group SL 2), we ins... more Using covering theory approach (zero-curvature representations with the gauge group SL 2), we insert the spectral parameter into the Gauss-Mainardi-Codazzi equations in Tchebycheff and geodesic coordinates. For each choice, four integrable systems are obtained.

Contemporary mathematics, 1998

arXiv (Cornell University), Oct 25, 2000

In the context of the cohomological deformation theory, infinitesimal description of one-parametr... more In the context of the cohomological deformation theory, infinitesimal description of one-parametric families of Bäcklund transformations of special type including classical examples is given. It is shown that any family of such a kind evolves in the direction of a nonlocal symmetry shadow in the sense of [10].

arXiv (Cornell University), Jan 3, 2014

In the framework of the theory of differential coverings [2], we discuss a general geometric cons... more In the framework of the theory of differential coverings [2], we discuss a general geometric construction that serves the base for the so-called Lax pairs containing differentiation with respect to the spectral parameter [4]. Such kind of objects arise, for example, when studying integrability properties of equations like the Gibbons-Tsarev one [1]. 2010 Mathematics Subject Classification. 37K10. Key words and phrases. Geometry of PDEs, differential coverings. I am grateful to the Mathematical Institute of the Silesian University in Opava for support and comfortable working condition.

arXiv (Cornell University), Aug 31, 1998

Proposition 1.2. Let P, Q and R be A-modules. Then: (1) If ∆ 1 ∈ Diff k (P, Q) and ∆ 2 ∈ Diff l (... more Proposition 1.2. Let P, Q and R be A-modules. Then: (1) If ∆ 1 ∈ Diff k (P, Q) and ∆ 2 ∈ Diff l (Q, R) are two differential operators, then their composition ∆ 2 • ∆ 1 lies in Diff k+l (P, R). (2) The maps i •,+ : Diff k (P, Q) → Diff + k (P, Q), i +,• : Diff + k (P, Q) → Diff k (P, Q) generated by the identical map of Hom k (P, Q) are differential operators of order ≤ k.

Texts and monographs in symbolic computation, 2017

Texts and monographs in symbolic computation, 2017

Texts and monographs in symbolic computation, 2017

Texts and monographs in symbolic computation, 2017

Texts and monographs in symbolic computation, 2017

The tangent covering is an equation naturally related to the initial equation \(\mathbb {E}\) and... more The tangent covering is an equation naturally related to the initial equation \(\mathbb {E}\) and which covers the latter and plays the same role in the category of differential equations that the tangent bundle plays in the category of smooth manifolds. It is used to construct recursion operators for symmetries of \(\mathbb {E}\) and symplectic structures on \(\mathbb {E}\). In this chapter we give the solution to Problem 1.18 and also prepare a basis to solution of Problems 1.20 (Chap. 7) and 1.22 (Chap. 8).

Texts and monographs in symbolic computation, 2017

A variational Poisson structure on a differential equation \(\mathcal {E}\) is a \(\mathcal {C}\)... more A variational Poisson structure on a differential equation \(\mathcal {E}\) is a \(\mathcal {C}\)-differential operator that takes cosymmetries of \(\mathcal {E}\) to its symmetries and possesses the necessary integrability properties. In the literature on integrable systems, Poisson structures are traditionally called Hamiltonian operators. We expose here the computational theory of local variational Poisson structures for normal equations. In this chapter the solutions of Problems 1.24, 1.25, 1.26, and 1.28 is presented.

This is an overview of recent results obtained by S. Igonin, P. Kersten, and A. Verbovetsky in co... more This is an overview of recent results obtained by S. Igonin, P. Kersten, and A. Verbovetsky in collaboration with the author and related to using of nonlocal constructions in geometry of partial di®erential equations. For general references concerning geometry of PDE see [1, 7]. Let E J1() 1¡¡! M be an in¯nitely prolonged di®erential equation con-sidered as a submanifold in an appropriate manifold of in¯nite jets. Then E is endowed with a natural ¯nite-dimensional integrable distribution (the Cartan dis-tribution denoted by C) locally spanned by the total derivatives. A ¯ber bundle ¿ : ~E! E is called a covering over E if (a) ~E is endowed with an integrable distri-bution ~C, dim ~C = dim C and (b) ¿ ¤ ~Cy = C¿(y) for any y 2 ~E. A 1 ± ¿-vertical vector ¯eld X is called a nonlocal symmetry of E if it preserves ~C. Nonlocal symmetries can be expressed in ¯nite terms rather rarely. A good (and rather useful) substitute is the notion of a shadow (that is often mixed up with nonlocal sy...

Astrakhan. In: Symmetries: Theoretical and Methidological Aspects, Astrakhan, 2007, pp. 46–53.

Encyclopedia of Complexity and Systems Science, 2009

arXiv: Exactly Solvable and Integrable Systems, 2020

We construct a three-component system of PDEs describing dynamics of van der Walls gas in one-dim... more We construct a three-component system of PDEs describing dynamics of van der Walls gas in one-dimensional nozzle. The group of conservation laws for this system is described. We also ompute the Lie algebras of point symmetries and present group classification. Exact invariant solutions are discussed.

一般社団法人電子情報通信学会, Jul 3, 2008