Acta Applicandae Mathematica

, Volume 41, Issue 1, pp 135-144

First online:

Conservation laws and the variational bicomplex for second-order scalar hyperbolic equations in the plane

  • Ian M. AndersonAffiliated withDepartment of Mathematics, Utah State University
  • , Niky KamranAffiliated withDepartment of Mathematics, McGill University

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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.

Mathematics subject classifications (1991)

58G16 35A30 35L65

Key words

variational bicomplex hyperbolic second-order equations conservation laws