On the properties of solutions of a system of two nonlinear differential equations associated with the Josephson model
type: Item
instance of: scholarly article
title: On the properties of solutions of a system of two nonlinear differential equations associated with the Josephson model
zbMATH Open document ID: 1545.34116
author: V. V. Tsegel'nik
published in: Theoretical and Mathematical Physics
publication date: 2024-06-13T00:00:00Z
review text: The analytical properties of solutions of the system\N\[\N\begin{aligned}\Nz^{2}u'&=z^{2}v+(1-l)zu-u^{2}v,\\\Nz^{2}v'&=-z^{2}u+lzv+uv^{2}(l=\mathrm{constant})\N\end{aligned}\N\]\Nare studied in the paper. It is shown that the solutions of the system have the Painlevé properties. Furthermore, this system can be reduced to the fifth Painlevé equation.
reviewed by: Mykola Grygorenko
Mathematics Subject Classification ID: 34M55
Mathematics Subject Classification ID: 34M25
zbMATH DE Number: 7864571
zbMATH Keywords: third Painlevé equation
zbMATH Keywords: fifth Painlevé equation
zbMATH Keywords: Bäcklund transformation
zbMATH Keywords: Josephson model
MaRDI profile type: Publication
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DOI: 10.1134/S0040577924040020
description: scientific article; zbMATH DE number 7864571