Skip to main content

Cosymmetries

  • Chapter
  • First Online:
  • 526 Accesses

Part of the book series: Texts & Monographs in Symbolic Computation ((TEXTSMONOGR))

Abstract

The most common use of cosymmetries is related to construction of conservation laws, because the generating functions of conservation laws are cosymmetries, but they also play an important role in the theory of the tangent (Chap. 6) and the cotangent (Chap. 9) coverings. We give the solution to Problems 1.8, 1.9, 1.10 and 1.13 in this chapter.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   89.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   119.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Anderson, I.M., Kamran, N.: Conservation laws and the variational bicomplex for second-order scalar hyperbolic equations in the plane. Acta Appl. Math. 41(1), 135–144 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bocharov, A.V., Chetverikov, V.N., Duzhin, S.V., Khorkova, N.G., Krasilshchik, I.S., Samokhin, A.V., Torkhov, Y.N., Verbovetsky, A.M., Vinogradov, A.M.: In: Krasilshchik, I.S., Vinogradov, A.M. (eds.) Symmetries and Conservation Laws for Differential Equations of Mathematical Physics. Monograph. American Mathematical Society, Providence (1999)

    Google Scholar 

  3. Khor’kova, N.G.: On the \(\mathcal {C}\)-spectral sequence of differential equations. Differ. Geom. Appl. 3(3), 219–243 (1993)

    Google Scholar 

  4. Khorkova, N.G.: Conservation laws and nonlocal symmetries. Math. Notes 44, 562–568 (1989)

    Google Scholar 

  5. Vinogradov, A.M.: The \(\mathcal {C}\)-spectral sequence, Lagrangian formalism, and conservation laws. I. The linear theory. II. The nonlinear theory. J. Math. Anal. Appl. 100, 1–129 (1984)

    Google Scholar 

  6. Vinogradov, A.M.: Cohomological Analysis of Partial Differential Equations and Secondary Calculus. American Mathematical Society, Providence (2001)

    Book  MATH  Google Scholar 

  7. Zhiber, A.V., Sokolov, V.V.: Exactly integrable hyperbolic equations of Liouville type. Russ. Math. Surv. 56(1), 61–101 (2001). https://doi.org/10.4213/rm357

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Krasil’shchik, J., Verbovetsky, A., Vitolo, R. (2017). Cosymmetries. In: The Symbolic Computation of Integrability Structures for Partial Differential Equations. Texts & Monographs in Symbolic Computation. Springer, Cham. https://doi.org/10.1007/978-3-319-71655-8_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-71655-8_4

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-71654-1

  • Online ISBN: 978-3-319-71655-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics