From additional symmetries to linearization of Virasoro symmetries

PHYSICA D-NONLINEAR PHENOMENA

卷:249

Article

Wu, Chao-Zhong

关键词: Additional symmetry;    Adler-Shiota-van Moerbeke formula;    Two-component BKP hierarchy;    Drinfeld-Sokolov hierarchy;    Virasoro symmetry;   

DOI  :  10.1016/j.physd.2013.01.005

来源: Elsevier

【 摘 要 】

We construct the additional symmetries and derive the Adler-Shiota-van Moerbeke formula for the two-component BKP hierarchy. Considered as certain reductions of the two-component BKP hierarchy, the Drinfeld-Sokolov hierarchies of type D are proved to possess symmetries written as the linear action of a series of 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. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free