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

Shibaji Roy·Sudhakar Panda
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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 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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Shibaji Roy, Sudhakar Panda. 1992-08-26. The Lax Operator Approach for the Virasoro and the W-Constraints in the Generalized KdV Hierarchy. https://doi.org/10.1142/s0217751x93001387

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