Geodesic
On the properties of solutions of a system of two nonlinear differential equations associated with the Josephson model
Teoretičeskaâ i matematičeskaâ fizika, Tome 219 (2024) no. 1, pp. 12-16 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $$ \biggl(\frac{(1-l)^2}{8}, -\frac{(1-l)^2}{8},0,-2\biggr), \; \biggl(\frac{l^2}{8}, -\frac{l^2}{8},0,-2\biggr). $$ 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.
Mots-clés : third Painlevé equation, fifth Painlevé equation
Keywords: Bäcklund transformation, Josephson model. 
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V. V. Tsegel'nik. On the properties of solutions of a system of two nonlinear differential equations associated with the Josephson model. Teoretičeskaâ i matematičeskaâ fizika, Tome 219 (2024) no. 1, pp. 12-16. http://geodesic.mathdoc.fr/item/TMF_2024_219_1_a1/

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