论与约瑟夫森模型相关的两个非线性微分方程系的解的性质

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Theoretical and Mathematical Physics Pub Date : 2024-04-26 DOI:10.1134/S0040577924040020

V. V. Tsegelnik

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引用次数: 0

摘要

摘要我们研究了与过阻尼约瑟夫森模型相关的带有任意参数 $l$ 的两个一阶非线性微分方程系统解的解析性质。我们把这个系统简化为一个微分方程系统，它等价于参数集为 $$\biggl(\frac{(1-l)^2}{8}, -\frac{(1-l)^2}{8},0,-2\biggr), \; \biggl(\frac{l^2}{8}, -\frac{l^2}{8},0,-2\biggr) 的第五个潘列夫方程。$$ 我们证明，参数为 $(-2l,2l-2,1,-1)$的第三个潘列夫方程的解可以表示为第五个潘列夫方程的解（参数为上述序列中的参数）的两个线性分数变换之比，这两个线性分数变换通过贝克隆变换连接起来。

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On the properties of solutions of a system of two nonlinear differential equations associated with the Josephson model

We investigate the analytic properties of solutions of a system of two first-order nonlinear differential equations with an arbitrary parameter $l$ associated with an overdamped Josephson model. We reduce this system to a system of differential equations that is equivalent to the fifth Painlevé equation with the sets of parameters

We show that the solution of the third Painlevé equation with the parameters $(-2l, 2l-2,1,-1)$ can be represented as the ratio of two linear fractional transformations of the solutions of the fifth Painlevé equation (with the parameters in the above sequence) connected by a Bäcklund transformation.

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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.