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arXiv · 1112.0246

From Additional Symmetries to Linearization of Virasoro Symmetries

Chao-Zhong Wu
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Abstract

We construct the additional symmetries and derive the Adler-Shiota-van Moerbeke formula for the two-component BKP hierarchy. We also show that the Drinfeld-Sokolov hierarchies of type D, which are reduced from the two-component BKP hierarchy, possess symmetries written as the action of a series of linear Virasoro operators on the tau function. It results in that the Drinfeld-Sokolov hierarchies of type D coincide with Dubrovin and Zhang's hierarchies associated to the Frobenius manifolds for Coxeter groups of type D, and that every solution of such a hierarchy together with the string equation is annihilated by certain combinations of the Virasoro operators and the time derivations of the hierarchy.

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Chao-Zhong Wu. 2011-12-01. From Additional Symmetries to Linearization of Virasoro Symmetries. https://doi.org/10.1016/j.physd.2013.01.005

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