The Lax Operator Approach for the Virasoro and the W-Constraints in the Generalized KdV Hierarchy

Details The Lax Operator Approach for the Virasoro and the W-Constraints in the Generalized KdV Hierarchy The Lax Operator Approach for the Virasoro and the W-Constraints in the Generalized KdV Hierarchy

1992-08-26

arxiv.org/abs/hep-th/9208065v1

Int. J. Mod. Phys. A8 (1993) 3457

Physics

High Energy Physics

High Energy Physics - Theory

26, IC-92-226

Scientific paper

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 partiacular, we consider the KdV and Boussinesq hierarchy to show that the Virasoro and 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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