Minimal algebraic solutions of the sixth Painlevé equation

IF 1.1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Theoretical and Mathematical Physics Pub Date : 2025-09-26 DOI:10.1134/S0040577925090053

R. Conte

引用次数: 0

Abstract

For each of the forty-eight exceptional algebraic solutions \(u(x)\) of the sixth Painlevé equation, we build the algebraic curve \(P(u,x)=0\) of a degree conjectured to be minimal, and then we give an optimal parametric representation of it. This degree is equal to the number of branches, except for fifteen solutions.

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第六阶painlevleve方程的最小代数解

对于第六个painlev方程的48个例外代数解\(u(x)\)中的每一个，我们都构建了一个猜想最小度的代数曲线\(P(u,x)=0\)，然后我们给出了它的最优参数表示。除了15个解外，这个度数等于分支数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Theoretical and Mathematical Physics 物理-物理：数学物理

CiteScore

1.60

自引率

20.00%

发文量

103

审稿时长

4-8 weeks

期刊介绍： Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems. Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.