论文标题
关于非平稳PIIN层次结构的对称性及其应用
On symmetries of the non-stationary PIIn hierarchy and their applications
论文作者
论文摘要
在目前的论文中，我们研究了非平台第二parchlevé层次结构$ \ text {p} _ \ text {ii}^{（n）} $的自动 - bäcklund转换，这取决于$ n $ parameters：a parameter $α_n$和times $ times $ t_1，\ t_1，\ dots $ t_1，\ dots，\ dots，\ dots，t_ t _ {n-1-1} $。使用发电机$ s^{（n）} $和$ r^{（n）} $的这些对称性，我们已经构造了一个与$ n $ th成员相关联的offine weyl offine weyl offine weyl offine weyl offine weyl offine weyl grout $ w^{（n）} $。我们通过yablonskii-vorobiev-type polyenmials $ u_m^{（n）}（z）$确定了$ \ text {p} _ \ text {ii}^{（n）} $合理解决方案。我们提出了yablonskii-vorobiev-type多项式与多项式$τ$ - functions $τ_m^{（n）}（z）$之间的相关性，并以jacobi-trudi形式找到了他们的决定性表示。
In the current paper we study auto-Bäcklund transformations of the non-stationary second Painlevé hierarchy $\text{P}_\text{II}^{(n)}$ depending on $n$ parameters: a parameter $α_n$ and times $t_1, \dots, t_{n-1}$. Using generators $s^{(n)}$ and $r^{(n)}$ of these symmetries, we have constructed an affine Weyl group $W^{(n)}$ and its extension $\tilde{W}^{(n)}$ associated with the $n$-th member considered hierarchy. We determined $\text{P}_\text{II}^{(n)}$ rational solutions via Yablonskii-Vorobiev-type polynomials $u_m^{(n)} (z)$. We brought out a correlation between Yablonskii-Vorobiev-type polynomials and polynomial $τ$-functions $τ_m^{(n)} (z)$ and found their determinant representation in the Jacobi-Trudi form.
