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

Ian M. Anderson and Niky Kamran
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Ian M. Anderson: Utah State University, Department of Mathematics
Niky Kamran: McGill University, Department of Mathematics

A chapter in Geometric and Algebraic Structures in Differential Equations, 1995, pp 135-144 from Springer

Abstract: 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.

Keywords: Spectral Sequence; Hyperbolic Equation; Contact Form; Linear Hyperbolic Equation; Laplace Invariant (search for similar items in EconPapers)
Date: 1995
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-0179-7_8

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DOI: 10.1007/978-94-009-0179-7_8

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