• DOI:10.1007/s11005-021-01465-3
• Corpus ID: 222090542

On an extension of the generalized BGW tau-function

@article{Yang2020OnAE,
  title={On an extension of the generalized BGW tau-function},
  author={Di Yang and Chun Hui Zhou},
  journal={Letters in Mathematical Physics},
  year={2020},
  volume={111}
}

• Di Yang, C. Zhou
• Published 1 October 2020
• Mathematics
• Letters in Mathematical Physics

For an arbitrary solution to the Burgers–KdV hierarchy, we define the tau-tuple (τ1,τ2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\tau _1,\tau _2)$$\end{document} of the solution. We show that the product τ1τ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau _1\tau _2$$\end{document} admits Buryak’s residue formula. Therefore, according to Alexandrov’s theorem, τ1τ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau _1\tau _2$$\end{document} 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 τ1τ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau _1\tau _2$$\end{document} explicitly in terms of those for τ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau _1$$\end{document}. Applications to the analogous open extension of the generalized BGW tau-function and to the open partition function are given.