Authors: P. KERSTEN, I. KRASIL'SHCHIK, A. VERBOVETSKY
An 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.
To compile source files (.tex) one needs the title page style files titlatex.tex.