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Conservation Laws and the Variational Bicomplex for Second-Order Scalar Hyperbolic Equations in the Plane

In: Geometric and Algebraic Structures in Differential Equations

Author

Listed:
  • Ian M. Anderson

    (Utah State University, Department of Mathematics)

  • Niky Kamran

    (McGill University, Department of Mathematics)

Abstract

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.

Suggested Citation

  • Ian M. Anderson & Niky Kamran, 1995. "Conservation Laws and the Variational Bicomplex for Second-Order Scalar Hyperbolic Equations in the Plane," Springer Books, in: P. H. M. Kersten & I. S. Krasil’Shchik (ed.), Geometric and Algebraic Structures in Differential Equations, pages 135-144, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-0179-7_8
    DOI: 10.1007/978-94-009-0179-7_8
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