TOROIDAL LIE ALGEBRAS AND SOME DIFFERENTIAL EQUATIONS OF TODA TYPE

Abstract

We deduce a recursive system of partial differential equations from the toroidal Lie algebra associated to a simple Lie algebra. Such a recursive system starts from the corresponding classical Toda field equations. For each truncated system we describe its Hamiltonian formalism using Gel'fand–Dikii's differential polynomial algebras, and some nontrivial local integrals are given.