**DIPS 6/2002**[tex source, PostScript, PDF file, dvi]-
**Title:**Hamiltonian operators and -coverings.**Authors:**P. KERSTEN, I. KRASIL'SHCHIK, A. VERBOVETSKYAn efficient method to construct Hamiltonian structures for nonlinear evolution equations is described. It is based on the notions of variational Schouten bracket and the -covering. The latter serves the role of the cotangent bundle in the category of nonlinear evolution PDEs. 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. As an illustrative example, the classical Boussinesq equation is considered. For both equations, new nonlocal Hamiltonian operators are constructed.

Revised version from August 3, 2003. 25 pages, LaTeX2e.

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