Conservation laws and the variational bicomplex for second-order scalar hyperbolic equations in the plane
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
In this paper, we announce several new results concerning the cohomology of the variational bicomplex for a second-order scalar hyperbolic equation in the plane. These cohomology groups are represented by the conservation laws, and certain form-valued generalizations, for the equation. Our methods are based upon the introduction of an adapted coframe for the the variational bicomplex which is constructed by generalizing the classical Laplace transformation used to integrate certain linear hyperbolic equations in the plane.
- Andersen, M. Introduction to the variational bicomplex. In: Gotay, M., Marsden, J., Moncrief, V. eds. (1992) Mathematical Aspects of Classical Field Theory. Amer. Math Soc., Providence, pp. 51-73
- Anderson, Ian M. and Kamran, N.: The variational bicomplex for second order scalar partial differential equations in the plane, Centre de recherches mathématiques, Technical report, September 1994.
- Anderson, Ian M. and Kamran, N.: The variational bicomplex for hyperbolic second order scalar partial differential equations in the plane (submitted May 1995).
- Bryant, R. L. and Griffiths, P. A.: Characteristic cohomology of differential systems, I: General theory, Duke University, Mathematics Preprint Series, January, 1993.
- Bryant, R. L. and Griffiths, P. A.: Characteristic cohomology of differential systems, II: Conservation laws for a class of parabolic equations, Duke University, Mathematics Preprint Series, January, 1993.
- Darboux, G. (1896) Leçons sur la théorie générale des suraces et les applications géométriques du calcul infinitésimal. Gauthier-Villars, Paris
- Forsyth, A. (1959) Theory of Differential Equations, Vol. 6. Dover, New York
- Goursat, E. (1896) Leçon sur l'intégration des équations aux dérivées partielles du second ordre á deux variables indépendantes. Hermann, Paris
- Olver, P. J. (1986) Applications of Lie Groups to Differential Equations. Springer, New York
- Tsujishita, T. (1982) On variation bicomplexes associated to differential equations. Osaka J. Math. 19: pp. 311-363
- Tsujishita, T. (1989) Formal geometry of systems of differential equations. Sugaku Exposition 2: pp. 1-40
- Vinogradov, A. M. (1984) The C-spectral sequence, Lagrangian formalism and conservation laws, I, II. J. Math. Anal. Appl. 100: pp. 1-129
- Conservation laws and the variational bicomplex for second-order scalar hyperbolic equations in the plane
Acta Applicandae Mathematica
Volume 41, Issue 1-3 , pp 135-144
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- variational bicomplex
- hyperbolic second-order equations
- conservation laws
- Industry Sectors