C. Morosi, Politecnico di Milano, Italy, CARMOR@mate.polimi.it, L. Pizzocchero, Univ. di Milano, Italy, PIZZOCCHERO@elanor.mat.unimi.it
On the continuous limit of integrable lattices III. Kupershmidt systems and 
sl(N+1) KdV theories.
(310K, postscript)

ABSTRACT.  We discuss the connection between the zero-spacing limit of 
the N fields Kupershmidt lattice and the KdV type theory corresponding
to the Lie algebra sl(N+1). The case N=2 is worked out in most detail,
recovering from the limit process the Boussinesq theory with its
infinitely many commuting vector fields, their Lax pairs and
Hamiltonian formulations. The "recombination method" proposed here 
to derive the Boussinesq hierarchy from the limit of
the N=2 Kupershmidt system works in principle for arbitrary N.