Acta Applicandae Mathematica

, Volume 41, Issue 1, pp 135–144

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


  • Ian M. Anderson
    • Department of MathematicsUtah State University
  • Niky Kamran
    • Department of MathematicsMcGill University

DOI: 10.1007/BF00996109

Cite this article as:
Anderson, I.M. & Kamran, N. Acta Appl Math (1995) 41: 135. doi:10.1007/BF00996109


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)


Key words

variational bicomplexhyperbolic second-order equationsconservation laws
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© Kluwer Academic Publishers 1995