Abstract
We show directly in the Lax operator approach how the Virasoro and W-constraints on the τ-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.
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