论文标题
从Painlevé到Zakharov-Shabat及以后：Fredholm的决定因素和全差异层次结构
From Painlevé to Zakharov-Shabat and beyond: Fredholm determinants and integro-differential hierarchies
论文作者
论文摘要
由于在随机整合性的背景下，弗雷德霍尔姆的决定因素越来越频繁，因此我们在许多出现的集成系统中揭示了一个共同框架的存在。这是由方程式的准全面层次结构组成，部分统一了对PainlevéII层次结构的全面差异性概括，Kardar-Parisi-Zhang方程的有限时间解决方案，在有限温度下的多临界费米和Zakharov Synememelt seem ersem e enseme enter enter enseme enter enseme enter enter ene a lar a lar a lar a lar a lar a lar a lar a lar a。作为副产品，我们从弗雷德尔姆（Fredholm）的决定因素方面获得了Zakharov-Shabat系统逆散射变换的明确唯一解决方案。
As Fredholm determinants are more and more frequent in the context of stochastic integrability, we unveil the existence of a common framework in many integrable systems where they appear. This consists in a quasi-universal hierarchy of equations, partly unifying an integro-differential generalization of the Painlevé II hierarchy, the finite-time solutions of the Kardar-Parisi-Zhang equation, multi-critical fermions at finite temperature and a notable solution to the Zakharov-Shabat system associated to the largest real eigenvalue in the real Ginibre ensemble. As a byproduct, we obtain the explicit unique solution to the inverse scattering transform of the Zakharov-Shabat system in terms of a Fredholm determinant.
