扩展的第二潘列维层次：自贝克伦德变换和特殊积分

IF 2.4 2区数学 Q1 MATHEMATICS

Journal of Differential Equations Pub Date : 2024-11-26 DOI:10.1016/j.jde.2024.11.017

P.R. Gordoa, A. Pickering

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引用次数: 0

摘要

我们回到前一篇论文中对扩展的第二潘列维层次结构的研究。对于这个层次，我们给出了一个新的局部自BT。我们还广泛讨论了使用自BT迭代构造解和特殊积分的问题。此外，我们还证明了可以为特殊积分提供 Lax 对。尽管这实际上是一种很普遍的情况，但以前似乎还没有给出过特殊积分的 Lax 对。在我们给出 Lax 对的方程中，有科斯格罗夫（Cosgrove）的例子，也有查兹（Chazy）的经典 Painlevé 分类结果。

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The extended second Painlevé hierarchy: Auto-Bäcklund transformations and special integrals

We return to our study of the extended second Painlevé hierarchy presented in a previous paper. For this hierarchy we give a new local auto-BT. We also give an extensive discussion of the iterative construction of solutions and special integrals using auto-BTs. Furthermore, we show that Lax pairs can be provided for special integrals. Even though this will, in fact, be the case quite generally, it seems that Lax pairs for special integrals have not been given previously. Amongst the equations for which we present Lax pairs are examples due to Cosgrove and, in classical Painlevé classification results, Chazy.

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来源期刊

Journal of Differential Equations 数学-数学

CiteScore

4.40

自引率

8.30%

发文量

543

审稿时长

9 months

期刊介绍： The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: • Mathematical control theory • Ordinary differential equations • Partial differential equations • Stochastic differential equations • Topological dynamics • Related topics