A FRACTIONAL KdV HIERARCHY (original) (raw)

We construct a new system of integrable non-linear differential equations associated with the operator algebra W (2) 3 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 (l) N operator algebras with arbitrary N and l.