- 98-20 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 II. Volterra systems and
Jan 16, 98
(auto. generated ps),
of related papers
Abstract. A connection is suggested between the zero-spacing limit of a
generalized N-fields Volterra (V_N) lattice and the KdV-type theory
which is associated, in the Drinfeld-Sokolov classification, to the simple
Lie algebra sp(N). As a preliminary step, the results of the previous
paper  are suitably reformulated and identified as the realization
for N=1 of the general scheme proposed here.
Subsequently, the case N=2 is analyzed in full detail; the
infinitely many commuting vector fields of the V_2 system (with their
Hamiltonian structure and Lax formulation) are shown to give in the
continuous limit the homologous sp(2) KdV objects, through
conveniently specified operations of field rescaling and recombination.
Finally, the case of arbitrary N is attacked, showing how to obtain
the sp(N) Lax operator from the continuous limit of the V_N system.