painleve3方程sinh-Gordon约简奇异渐近性的非线性最陡下降方法

IF 1.3 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL Letters in Mathematical Physics Pub Date : 2025-01-13 DOI:10.1007/s11005-024-01892-y

Alexander R. Its, Kenta Miyahara, Maxim L. Yattselev

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引用次数: 0

摘要

在tt*-Toda方程最简单的情况下，研究了sinh-Godron painleveiii （\(D_6\)）方程实解\( x>0 \)的大、小x渐近性。这些解通过相应黎曼-希尔伯特问题的一元数据被参数化。这种统一的方法提供了所考虑的解在原点和无穷远处的行为之间的联系公式。

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The non-linear steepest descent approach to the singular asymptotics of the sinh-Gordon reduction of the Painlevé III equation

Motivated by the simplest case of tt*-Toda equations, we study the large and small x asymptotics for \( x>0 \) of real solutions of the sinh-Godron Painlevé III(\(D_6\)) equation. These solutions are parametrized through the monodromy data of the corresponding Riemann–Hilbert problem. This unified approach provides connection formulae between the behavior at the origin and infinity of the considered solutions.

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来源期刊

Letters in Mathematical Physics 物理-物理：数学物理

CiteScore

2.40

自引率

8.30%

发文量

111

审稿时长

3 months

期刊介绍： The aim of Letters in Mathematical Physics is to attract the community''s attention on important and original developments in the area of mathematical physics and contemporary theoretical physics. The journal publishes letters and longer research articles, occasionally also articles containing topical reviews. We are committed to both fast publication and careful refereeing. In addition, the journal offers important contributions to modern mathematics in fields which have a potential physical application, and important developments in theoretical physics which have potential mathematical impact.