Diffiety Sophus Lie e-library Last updated April 12, 2007 The aim of the diffiety e-library is to allow open access to the most interesting diffiety literature, at first to papers of the Diffiety Institute members published at pre-electronical epoch. We hope to increase it permanently. All materials here are for noncommercial use only. We kindly request not to copy them on other sites and, if necessary, restrict yourself to giving references to our site. Almost all files below are in the djvu-format. To download djvu-viewer see LizardTech download site. Modern papers Modern books (in Russian) Classical works (Sophus Lie, Gaston Darboux, Elie Cartan, Tullio Levi-Civita, Riemann)

Modern papers

1995

• Khor'kova N. G., Verbovetsky A.M. - On Symmetry Subalgebras and Conservation Laws for the κ-ε Turbulence Model and the Navier-Stokes Equations. - - AMS. Translations. - Ser. 2. - v. 167. (1995), p. 61-90.
• Krasil'shchik I., P.H.M. Kersten - Graded Froelicher - Nijenhuis brackets and the theory of recursion operators for super differential equations - in The Interplay between Differential Geometry and Differential equations, Advances in the Mathematical Sciences, 24, Amer. Math. Soc., Providence RI, 1995.
• Vinogradov M. M. - Coconnections and integral forms - Soviet Math. Dokl. 50 (1995), No. 2, 229-233.

  1994

• Vinogradov A. M. - From symmetries of partial differential equations towards secondary ("quantized") calculus , - J. Geom. and Phys., 14 (1994), 146-194.
• Modugno M., Vinogradov A. M. - Some variations on the notion of connection, - Annali di Matematica pyra ed applicata, 167 (1994), 33-71.

  1993

• Khor'kova N. G. - On the C-spectral sequence of differential equations. - Differential Geometry and its Applications. - 1993.- v.3. - p.219-243.

  1992

• Cabras A., Vinogradov A. M. - Extension of the Poisson bracket to differential forms and multi-vector fields, - J. Geom. and Phys., 9 (1992) 1, 75-100.
• Krasil'shchik I. S., Some new cohomological invariants of nonlinear differential equations, Differential Geometry and Its Appl., 2 (1992) no. 4.
• Krasil'shchik I. S., Differential operators of constant growth and Jacobi structures of infinite order - Publ. IRMA 30 (1992), no. XI, Lille.
• Verbovetsky A. M., Vinogradov A. M., Gessler, D. M. - Scalar differential invariants and characteristic classes of homogeneous geometric structures, - (Russian) Mat. Zametki, 51 (1992), no. 6, 15-26. English translation in Math. Notes, 51 (1992), no. 5-6, 543-549.

  1991

• I. S. Krasil'shchik, - Supercanonical algebras and Schouten brackets, - (Russian) Mat. Zametki, Vol. 49 (1991), no. 6, pages 70-76. English translation in Math. Notes, 51 (1992), no. 5-6, 543-549.
• Vinogradov A. M. Scalar differential invariants, diffieties, and characteristic classes, - in: Francaviglia M. (Ed.), Mechanics, Analysis and Geometry: 200 Years after Lagrange, (1991), Elsvier, Amsterdam, 379-416.
• Chetverikov V. N., On the structure of integrable C-fields, "Diff.Geom.and Appl.", v.1, n.4 (1991) 309-325.
• Toru Tsujishita - Homological method of computing invariants of systems of differential equations - Differential geometry and its applications, 1 (1991), 3-34.
• Vinogradov M. M. - On a general algebraic theory of linear differential operators - Soviet Math. Dokl. 43 (1991), No. 2, 355-359.

  1989

• Krasil'shchik I. S., Vinogradov A. M. - Nonlocal trends in the geometry of differential equations: symmetries, conservation laws, and Baecklund transformations, - Acta Appl. Math., 15 (1989) 1-2, 161-209. Also in: Vinogradov A. M. (Ed.), Symmetries of Partial Differential Equations, (1989), Kluwer Academic Publishers, Dordrecht, Boston, London, 161-209.
• Toru Tsujishita - Compatibility of systems of super differential equations - J. Geom. and Phys., 6 No. 2 (1989), 170-213.
• A. M. Vinogradov - Symmetries and conservation laws of partial differential equations: basic notions and results. - Symmetries of partial differential equations. Part I, Acta Appl. Math., 15 (1989), no. 1-2, 3-21.
• V. N. Gusyatnikova, A. V. Samokhin, V. S. Titov, A. M. Vinogradov, V. A. Yumaguzhin - Symmetries and conservation laws of Kadomtsev-Pogutse equations (their computation and first applications). Symmetries of partial differential equations. - Symmetries of partial differential equations. Part I, Acta Appl. Math., 15 (1989), no. 1-2, 23-64.

  1988

• I. Krasil'shchik - Schouten bracket and canonical algebras - Lecture Notes in Math., Springer-Verlag, 1334, pp. 79-110, 1988.
• Vinogradov A. M., - An informal introduction to the geometry of jet spaces - Conference on Differential Geometry and Topology (Sardinia, 1988). Rend. Sem. Fac. Sci. Univ. Cagliari 58 (1988), suppl., 301-333.
• S. I. Senashov, A. M. Vinogradov, - Symmetries and conservation laws of 2-dimensional ideal plasticity, - Proc. Edinburgh Math. Soc., 31 (1988), 415-439.

  1988

• Vinogradov A. M. - Integrability and symmetries, - in Nonlinear waves. Structures and bifurcations, Moscow, Nauka, 1987, pp. 279-290 (Russian).

  1986

• Astashov A. M., Vinogradov A. M. - On the structure of Hamiltonian operator in field theory, - J. Geom. and Phys., 3 (1986), no. 2, 263-287.
• Vinogradov A. M. - Geometric singularities of solutions of nonlinear partial differential equations, - Differential geometry and its applications (Brno, 1986), 359-379, Math. Appl. (East European Ser.), 27, Reidel, Dordrecht-Boston, MA, 1987.

  1985

• Gusyatnikova V. N., Vinogradov A. M., Yumaguzhin V. A. - Secondary differential operators, - J. Geom. and Phys., v. 2, No 2, (1985), 23-65.
• Vinogradov A. M.;, Gusyatnikova V. N., Yumaguzhin V. A. - Secondary differential operators, - Soviet Math. Dokl., vol. 32 (1985), No. 1.

  1984

• Vinogradov A. M., - Local symmetries and conservation laws, - Acta Appl. Math., 3 (1984), 21-78.
• Krasil'shchik I. S., Vinogradov A. M., - Nonlocal symmetries and the theory of coverings - an addendum to A. M. Vinogradov's Local symmetries and conservation laws, - Acta Appl. Math., 3 (1984), 79-96.
• Vinogradov A. M., Krasil'shchik I. S. - On the theory of nonlocal symmetries of nonlinear partial differential equations, - Soviet Math. Dokl., 29 (1984), No 2, pp. 337 - 341.
• Vinogradov A. M., - The C-spectral sequence, Lagrangian formalism, and conservation laws. I. The linear theory, - J. Math. Anal. Appl., v. 100 (1984), no. 1, 1-40.
• Vinogradov A. M., - The C-spectral sequence, Lagrangian formalism, and conservation laws. II. The nonlinear theory, - J. Math. Anal. Appl., v. 100 (1984), no. 1, 41-129.
• Vinogradov A. M. - Category of partial differential equations, - Lecture Notes in Math., 1108 (1984), Springer-Verlag, Berlin, 77-102.
• Vinogradov A. M. - The category of differential equations and its significance for physics, - in: Krupka D. (Ed.), Proc. Conf. Diff. Geom. Appl. (Brno, 1984), (1984), J.E. Purkyne Univ., Brno, Czechoslovakia, 289-301.

  1983

• Astashov A. M. - Normal forms of Hamiltonian operators in field theory - Soviet Math. Dokl., 27 No. 3 (1983), 685-689.

  1981

• A. M. Vinogradov - Geometry of nonlinear differential equations, - J. Sov. Math., 17 (1981), 1624-1649.
• Vinogradov A. M., Krasil'shchik I. S. - What is the Hamiltonian formalism? - London Math. Soc. Lect. Notes Ser., 60 (1981), Cambridge Univ. Press, London, 241-266.
• Vinogradov A. M., Kupershmidt B.A. - The structure of Hamiltonian mechanics, - London Math. Soc. Lect. Notes Ser., 60 (1981), Cambridge Univ. Press, London, 173-239.
• Bocharov A. V. - Spencer cohomology of an algebraic curve with coefficients in a normalization - Soviet Math. Dokl., 24 No. 3 (1981), 629-633.

  1980

• Vinogradov A. M.- The geometry of nonlinear differential equations - Problems in geometry, Vol. 11 (Russian), pp. 89-134, Akad. Nauk SSSR, VINITI, Moscow, 1980 (in Russian).
• I.S. Krasil'shchik - Hamiltonian cohomologies of canonical algebras - Soviet Math. Dokl., vol.21 (1980), No 2, pp. 625 - 629.
• A. M. Vinogradov, I.S. Krasil'shchik - A method of computing higher symmetries of nonlinear evolution equations and nonlocal symmetries - Soviet Math. Dokl., 22 (1980), 235-239.

  1979

• Vinogradov A. M. - Some homological systems associated with differential calculus over commutative algebras, - Russian Math. Surveys, 34 (1979) 6, 250-255.

  1978

• Vinogradov A. M. - A spectral system associated with a non-linear differential equation, and the algebro-geometric foundations of Lagrangian field theory with constraints, - Soviet Math. Dokl., 19 (1978), 144-148.
• Vinogradov A. M. - Hamiltonian structures in field theory, - Soviet Math. Dokl., 19 (1978), 790-794.
• Vinogradov M. M. - On De Rham and Spencer algebraic cohomology of smooth manifolds - Soviet Math. Dokl., vol.19, No 5, pp.1220 - 1224.

  1977

• Vinogradov A. M. - On the algebro-geometric foundations of Lagrangian field theory, - Soviet Math. Dokl., 18 (1977), 1200-1204.

  1976

• Goldschmidt H., Spencer D. C. - On the non-linear cohomology of Lie equations. I - Acta Math. 136 (1976), 103-170.
• Goldschmidt H., Spencer D. C. - On the non-linear cohomology of Lie equations. II - Acta Math. 136 (1976), 171-239.

  1974

• Spencer D. C. - Curvatures associated with differential operators, - Lecture Notes in Math., Vol. 392, Springer, Berlin, 1974, 64-75.

  1973

• Vinogradov A. M., - Multivalued solutions and a classification principle for differential equation, - Soviet Math. Dokl., 14 (1973), 661-665.

  1972

• Vinogradov A. M., - The logic algebra for the theory of linear differential operators, - Soviet Math. Dokl., 13 (1972), 1058-1062.

  1971

• Spencer D. C. - Flat differential operators, - Lecture Notes in Math., Vol. 184, Springer, Berlin, 1971,85-108.

  1970

• Spencer D. C. - Uncoupled overdetermined systems, Global Analysis (Proc. Sympos. Pure Math. Vol. 16, Berkeley, California, 1968), Amer. Math. Soc., 1970, 211-220.

  1969

• Spencer D. C. - Overdetermined systems of linear partial differential equations, - Bull. Amer.Math.Soc. 75 (1969), 179-239.

  1965

• L. Ehrenpreis, V. W. Guillemin, and S. Sternberg - On Spencer's Estimate for -Poincaré - Ann. of Math. 82 (1965), 128-138.

  1964

• V. W. Guillemin and S. Sternberg - An algebraic model of transitive algebraic geometry - Bull. Amer. Math. Soc., 70 (1964), 16-47.

  1962, 1965

• Spencer D. C. - Deformation of structures on manifolds defined by transitive, continuous pseudogroups. Parts I, II - Ann. of Math. 76 (1962), 306-445; Part III: Structures defined by elliptic pseudogroups - Ann. of Math. 81 (1965), 389-450.

Modern books

• Symmetries and Conservation Laws for Differential Equations of Mathematical Physics; edited by: Joseph Krasil'shchik, and Alexandre Vinogradov; authors: V. N. Chetverikov, A. B. Bocharov, S. V. Duzhin, N. G. Khor'kova, I. S. Krasil'shchik, A. V. Samokhin, Y. N. Torkhov, A. M. Verbovetsky, A. M. Vinogradov. Factorial Publ. House, 2005, 380 pages (in Russian).
  The second revised edition. English translation was published in 1999 by the AMS.
• Symmetries and Conservation Laws for Differential Equations of Mathematical Physics; edited by: Joseph Krasil'shchik, and Alexandre Vinogradov; authors: V. N. Chetverikov, A. B. Bocharov, S. V. Duzhin, N. G. Khor'kova, I. S. Krasil'shchik, A. V. Samokhin, Y. N. Torkhov, A. M. Verbovetsky, A. M. Vinogradov. Factorial Publ. House, 1997, 461 pages (in Russian).
  This is the first Russian edition of the book. English translation (with improvements and misprints corrected) was published in 1999 by the AMS. An updated second Russian edition was published in 2005.
• Smooth manifolds and observables by Jet Nestruev; authors: A. M. Astashev, A. V. Bocharov, S. V. Duzhin, A. B. Sossinsky, A. M. Vinogradov, M. M. Vinogradov; textbook, MCCME, Moscow, 2000-2003, 317 pages (in Russian).
  In the second (electronic) edition (likewise English one) new exercises were added (mostly) to the first half of the book, thus achieving a better balance with the second half. Besides, some typos and minor errors, noticed in the first edition, were corrected.
• Alekseevski D. V., Lychagin V. V., Vinogradov A. M. - Basic ideas and concepts of differential geometry, - Modern problems of mathematics: fundamental directions, Vol. 28, (1988), 298 p., Akad. Nauk SSSR, VINITI, Moscow (in Russian).
• Vinogradov A. M., Krasil'shchik I. S., Lychagin, V. V. - Introduction to the geometry of nonlinear differential equations, - (Russian) Nauka, Moscow, 1986. 336 pp.

Classical works

Cartan Elie

• Sur la structure des groupes de transformations finis et continus, - Thèse, Paris, Nony, 1894, 157 pages.

Darboux Gaston

• Leçons sur la théorie Générale des Surfaces et les applications géométriques du calcul infinitesimal, Deuxième partie. Les congruences et les équations linéaires aux dériviées partielles. Les lignes tracées sur les surfaces, - Paris, Gauthier-Villars, 1915, 579 pages.
• Leçons sur les Systèmes Orthogonaux et les Coordonnèes Curvilignes, - Deuxième èdition, complètèe, Paris, Gauthier-Villars, 1910, 570 pages.
• Leçons sur la théorie Générale des Surfaces et les applications géométriques du calcul infinitesimal, Troisième partie. Lignes géodésiques et courbure géodésique. Paramètres différentiels. Déformation des surfaces, - Paris, Gauthier-Villars, 1894, 512 pages.
• Leçons sur la théorie Générale des Surfaces et les applications géométriques du calcul infinitesimal, Quattrième partie. Déformation infiniment petite et représentation sphérique, - Paris, Gauthier-Villars, 1896, 548 pages.
• Leçons sur la théorie Générale des Surfaces et les applications géométriques du calcul infinitesimal, Première partie. Généralitiés. Coordonnées. Curvilignes Surfaces minima, - Paris, Gauthier-Villars, 1887, 514 pages.

Levi-Civita Tullio

• The Absolute Differential Calculus (Calculus of Tensors), - London and Glasgow, Blackie & son limited, I927, 450 pages.

Lie Sophus

• Gesammelte Abhandlungen. Fünfter band. Abhandlungen Füber die Theorie der Transformationsgruppen, - Druck und Verlag von B. G. Teubner, Leipzig, 1924, XII + 776 pages.
• Gesammelte Abhandlungen. Dritter band. Abhandlungen zur Theorie der Differentialgleichungen, - Druck und Verlag von B. G. Teubner, Leipzig, 1922, XVI + 789 pages.
• Geometrie der Berührungstraansformationen, - Erster Band, Leipzig, Druck und Verlag von B. G. Teubner, 1896, 695 pages.
• Vorlesungen über Differentialgleichungen mit Bekannten Infinitesimalen Transformationen, - Druck und Verlag von B. G. Teubner, Leipzig, 1891, XIV + 568 pages.

Riemann Bernhard

• Œeuvres mathématioues, - Paris, Gauthier-Villars et fils, 1898, XXXV + 453 pages.