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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
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)
Bocharov, A.V., Chetverikov, V.N., Duzhin, S.V., Khor′kova, N.G., Krasil′shchik, I.S., Samokhin, A.V., Torkhov, Y.N., Verbovetsky, A.M., Vinogradov, A.M.: In: Krasil′shchik, I.S., Vinogradov, A.M. (eds.) Symmetries and Conservation Laws for Differential Equations of Mathematical Physics. Monograph. American Mathematical Society, Providence (1999)
Khor′’kova, N.G.: On the \(\mathcal {C}\)-spectral sequence of differential equations. Differ. Geom. Appl. 3(3), 219–243 (1993)
Khor′kova, N.G.: Conservation laws and nonlocal symmetries. Math. Notes 44, 562–568 (1989)
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)
Vinogradov, A.M.: Cohomological Analysis of Partial Differential Equations and Secondary Calculus. American Mathematical Society, Providence (2001)
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
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG, part of Springer Nature
About this chapter
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)