论文标题
广义BGW tau功能的扩展
On an extension of the generalized BGW tau-function
论文作者
论文摘要
对于汉堡的任意解决方案-KDV层次结构，我们定义了解决方案的tau-tuple $（τ_1，τ_2）$。我们表明该产品$τ_1τ_2$允许Buryak的残留公式。因此，根据Alexandrov的定理，$τ_1τ_2$是KP层次结构的tau功能。然后，我们得出了与Tau功能相对应的Sato Grassmannian点的仿射坐标的公式，该公式与$τ_1$的tau功能相对应$τ_1τ_2$。给出了广义BGW tau功能和开放分区功能的类似开放扩展的应用。
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.
