A SUPERSYMMETRY APPROACH TO POISSON STRUCTURES
OVER DIFFERENTIAL EQUATIONS

I. S. Krasil'shchik

Key words: Nonlinear partial differential equations,
        supersymmetry, Poisson structures, Hamiltonian formalism.

1991 Math. Subject Classification: 35A30, 58F05, 58G05, 16W55, 81T60.

Abstract: An exposition of Poisson structures theory over nonlinear partial
differential equations is given. The approach is based on consideration
of $d_h$-invariant Hamiltonian formalism in the superalgebra $\La^*(\Ei)$,
$d_h$ being the horizontal differential.

Relations between supersymmetries and Poisson structures are established.
A local description of Poisson structures for the two cases
is given: $\Ei=\Ji(\pi)$ and $\CE$ being a system of evolution equations.