A Supersymmetry Approach To Poisson Structures Over Differential Equations

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 (E 1 ), d h being the horizontal differential. Relations between supersymmetriesand Poisson structures are established. A local description of Poisson structures for the two cases is given: E 1 = J 1 (ß) and E being a system of evolution equations