  An efficient method to construct Hamiltonian structures for nonlinear
evolution equations is described. It is based on the notions of variational
Schouten bracket and l*-covering. The latter serves the role of the cotangent
bundle in the category of nonlinear evolution PDEs. We first consider two
illustrative examples (the KdV equation and the Boussinesq system) and
reconstruct for them the known Hamiltonian structures by our methods. For the
coupled KdV-mKdV system, a new Hamiltonian structure is found and its
uniqueness (in the class of polynomial (x,t)-independent structures) is proved.
We also construct a nonlocal Hamiltonian structure for this system and prove
its compatibility with the local one.
