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.
Conservation Laws and the Variational Bicomplex for Second Order ScalarHyerbolic Equations in the PlaneActa Applicanda
Citation InformationConservation Laws and the Variational Bicomplex for Second Order Scalar Hyerbolic Equations in the Plane (with N. Kamran), Acta Applicanda 41(1995), 135–144.