THE LAX OPERATOR APPROACH FOR THE VIRASORO AND THE W-CONSTRAINTS IN THE GENERALIZED KDV HIERARCHY

We show directly in the Lax operator approach how the Virasoro and W-constraints on the tau-function arise in the p-reduced KP hierarchy or generalized KdV hierarchy. In particular, we consider the KdV and the Boussinesq hierarchy to show that the Virasoro and the W-constraints follow from the string equation by expanding the ''additional symmetry'' operator in terms of the Lax operator. We also mention how this method could be generalized for higher KdV hierarchies.