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arXiv 2010.004362020-10math-phmath.AGmath.MPnlin.SI

On an extension of the generalized BGW tau-function

Di Yang, Chunhui Zhou

备注：: Minor changes: improved presentations; corrected typos; added references. 21pages
DOI：: 10.1007/s11005-021-01465-3

英文摘要：

For an arbitrary solution to the Burgers--KdV hierarchy, we define the tau-tuple $(τ_1,τ_2)$ of the solution. We show that the product $τ_1τ_2$ admits Buryak's residue formula. Therefore, according to Alexandrov's theorem, $τ_1τ_2$ is a tau-function of the KP hierarchy. We then derive a formula for the affine coordinates for the point of the Sato Grassmannian corresponding to the tau-function $τ_1τ_2$ explicitly in terms of those for $τ_1$. Applications to the analogous open extension of the generalized BGW tau-function and to the open partition function are given.

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