ON THE CONTINUOUS LIMIT OF INTEGRABLE LATTICES II - VOLTERRA SYSTEMS AND SP(N) THEORIES

A connection is suggested between the zero-spacing limit of a generali zed N-fields Volterra (V-N) lattice and the KdV-type theory which is a ssociated, in the Drinfeld-Sokolov classification, to the simple Lie a lgebra sp(N). As a preliminary step, the results of the previous paper [1] 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 fiel ds of the V-2 system (with their Hamiltonian structure and Lax formula tion) are shown to give in the continuous Limit the homologous sp(2) K dV objects, through conveniently specified operations of field rescali ng and recombination. Finally, the case of arbitrary N is attacked, sh owing how to obtain the sp(N) Lax operator from the continuous limit o f the V-N system.