论文标题
完全非交通性的PainlevéII层次结构：与Fredholm决定因素有关的宽松和解决方案
A fully noncommutative Painlevé II hierarchy: Lax pair and solutions related to Fredholm determinants
论文作者
论文摘要
我们考虑了与$ n -$ th airy函数的矩阵版本相关的矩阵卷积运算符的弗雷德·霍尔姆（Fredholm）决定因素。利用可集成运营商的理论，我们将它们与完全非共同的PainlevéII层次结构联系起来，该层次结构通过Lenard Operators的矩阵有价值的版本定义。特别是，用于研究这些综合操作员的Riemann-Hilbert技术允许为每个层次结构的每个成员找到一对宽松对。最后，LAX矩阵的系数是按照这些矩阵有价值的Lenard运算符明确编写的，并且层次结构的某些解决方案是按照矩阵Airy卷积算子的平方的弗雷德霍尔姆决定因素编写的。
We consider Fredholm determinants of matrix convolution operators associated to matrix versions of the $n - $th Airy functions. Using the theory of integrable operators, we relate them to a fully noncommutative Painlevé II hierarchy, defined through a matrix valued version of the Lenard operators. In particular, the Riemann-Hilbert technique used to study these integrable operators allows to find a Lax pair for each member of the hierarchy. Finally, the coefficients of the Lax matrices are explicitely written in terms of these matrix valued Lenard operators and some solution of the hierarchy are written in terms of Fredholm determinants of the square of the matrix Airy convolution operators.
