The Cohomology of the Variational Bicomplex Invariant under the Symmetry Algebra of the Potential Kadomtsev-Petviashvili Equation

Abstract

The variational bicomplex of forms invariant under the symmetry algebra of the potential Kadomtsev-Petviashvili equation is described and the cohomology of the associated Euler-Lagrange complex is computed. The results are applied to a characterization problem of the Kadomtsev-Petviashvili equation by its symmetry algebra originally posed by David, Levi, and Winternitz.