论文标题
关于第四$ q $-painlevé方程的对称解决方案
On symmetric solutions of the fourth $q$-Painlevé equation
论文作者
论文摘要
Painlevé方程具有先验解决方案$ y（t）$，具有特殊的初始值，在复杂的$ t $平面中旋转或反射为对称。它们对应于可以在经典特殊功能方面明确解决的单肌问题。在本文中，我们展示了对于$ q $ - 差异方程式的这种解决方案的存在。我们专注于称为$ q \ textrm {p} _ {\ textrm {iv}} $或$ q {\ rm p}（a_5^{（1））$的对称解决方案。
The Painlevé equations possess transcendental solutions $y(t)$ with special initial values that are symmetric under rotation or reflection in the complex $t$-plane. They correspond to monodromy problems that are explicitly solvable in terms of classical special functions. In this paper, we show the existence of such solutions for a $q$-difference Painlevé equation. We focus on symmetric solutions of a $q$-difference equation known as $q\textrm{P}_{\textrm{IV}}$ or $q{\rm P}(A_5^{(1)})$ and provide their symmetry properties and solve the corresponding monodromy problem.
