A FRACTIONAL KDV HIERARCHY

We construct a new system of integrable nonlinear differential equations associated with the operator algebra W3(2) of Polyakov. Its members are fractional generalizations of KdV type flows corresponding to an alternative set of constraints on the 2-dim. SL(3) gauge connections. We obtain the first non-trivial examples by dimensional reduction from self-dual Yang-Mills and then generate recursively the entire hierarchy and its conserved quantities using a bi-Hamiltonian structure. Certain relations with the Boussinesq equation are also discussed together with possible generalizations of the formalism to SL(N) gauge groups and W(N)(l) operator algebras with arbitrary N and l.