Theoretical and Mathematical Physics

, Volume 185, Issue 2, pp 1557–1581 | Cite as

Conservation laws, differential identities, and constraints of partial differential equations



We consider specific cohomological properties such as low-dimensional conservation laws and differential identities of systems of partial differential equations (PDEs). We show that such properties are inherent to complex systems such as evolution systems with constraints. The mathematical tools used here are the algebraic analysis of PDEs and cohomologies over differential algebras and modules.


differential algebra conservation law differential identity differential constraint 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    V. V. Zharinov, Theor. Math. Phys., 68, 745–751 (1986).CrossRefADSMathSciNetMATHGoogle Scholar
  2. 2.
    V. V. Zharinov, Math. USSR-Sb., 71, 319–329 (1992).CrossRefMathSciNetMATHGoogle Scholar
  3. 3.
    V. V. Zharinov, Lecture Notes on Geometrical Aspects of Partial Differential Equations (Ser. Sov. East Eur. Math., Vol. 9), World Scientific, Singapore (1992).CrossRefMATHGoogle Scholar
  4. 4.
    V. V. Zharinov, Russian Acad. Sci. Sb. Math., 79, 33–45 (1994).MathSciNetGoogle Scholar
  5. 5.
    V. V. Zharinov, Proc. Steklov Inst. Math., 203, 391–402 (1995).MathSciNetGoogle Scholar
  6. 6.
    V. V. Zharinov, Theor. Math. Phys., 163, 401–413 (2010).CrossRefMATHGoogle Scholar
  7. 7.
    V. V. Zharinov, Theor. Math. Phys., 174, 220–235 (2013).CrossRefMathSciNetMATHGoogle Scholar
  8. 8.
    P. J. Olver, Applications of Lie Groups to Differential Equations, Springer, New York (1986, 1993).CrossRefMATHGoogle Scholar
  9. 9.
    E. R. Kolchin, Differential Algebra and Algebraic Groups, Acad. Press, New York (1973).MATHGoogle Scholar
  10. 10.
    J. F. Ritt, Differential Algebra, Dover, New York (1966).Google Scholar
  11. 11.
    S. Maclane, Homology, Springer, Berlin (1963).CrossRefMATHGoogle Scholar
  12. 12.
    T. Tsujishita, Osaka J. Math., 19, 311–363 (1982).MathSciNetMATHGoogle Scholar
  13. 13.
    A. M. Vinogradov, I. S. Krasil’shchik, and V. V. Lychagin, Introduction to the Geometry of Nonlinear Differential Equations [in Russian], Nauka, Moscow (1986)MATHGoogle Scholar
  14. 13a.
    I. S. Krasil’shchik, V. V. Lychagin, and A. M. Vinogradov, Geometry of Jet Spaces and Nonlinear Partial Differential Equations, Gordon and Breach, New York (1986).Google Scholar
  15. 14.
    R. Bott and L. W. Tu, Differential Forms in Algebraic Topology (Grad. Texts Math., Vol. 82), Springer, New York (1982).CrossRefMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Steklov Mathematical Institute of the Russian Academy of SciencesMoscowRussia

Personalised recommendations