论文标题
系统构建Painlevé-Type的非自主哈密顿方程。 ii。异构质宽松表示
Systematic construction of non-autonomous Hamiltonian equations of Painlevé-type. II. Isomonodromic Lax representation
论文作者
论文摘要
这是一系列文章中的第二篇文章，研究了Stäckel-Type Systems与Painlevé-Type系统之间的关系。在本文中，我们构建了弗罗贝尼乌斯（Frobenius）在frobenius的Stäckel-type系统的弗罗贝尼乌斯（Frobenius）可整合变形的Painlevé-type系统中构建等异构词的LAX表示。我们首先在所谓的磁性表示中构建了Painlevé-Type系统的等异散的LAX表示，然后使用多时间依赖的规范转换，我们还构建了非磁性表示中Painlevé-type Systems的等词质含量LAX表示。因此，我们证明了在第一部分中构建的Frobenius综合系统的确是Painlevé-Type。我们还提供了源自我们计划的所有一，二维和三维painlevé型系统的异构粒细胞的表示。基于这些结果，我们提出了从我们的施工中随后遵循的$ p_ {i} -p_ {iv} $的完整层次结构。
This is the second article in a suite of articles investigating relations between Stäckel-type systems and Painlevé-type systems. In this article we construct isomonodromic Lax representations for Painlevé-type systems found in the previous paper by Frobenius integrable deformations of Stäckel-type systems. We first construct isomonodromic Lax representations for Painlevé-type systems in the so called magnetic representation and then, using a multitime-dependent canonical transformation, we also construct isomonodromic Lax representations for Painlevé-type systems in the non-magnetic representation. Thus, we prove that the Frobenius integrable systems constructed in Part I are indeed of Painlevé-type. We also present isomonodromic Lax representations for all one-, two- and three-dimensional Painlevé-type systems originating in our scheme. Based on these results we propose complete hierarchies of $P_{I}-P_{IV}$ that follow from our construction.
