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Method of isomonodromic deformations for “degenerate” third Painlevé equation

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Abstract

To study the solutions of the equation (τuτ)τ=eu−eu which is a version of the “degenerate” third Painlevé equation we consider a linear ordinary differential equation in 3×3 matrices. By means of the monodromy data of this linear equation we parametrize the asymptotics of all solutions as τ→0, as well as the asymptotics of regular solutions of the nonlinear equation studied as τ→±∞.

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Authors
  1. A. V. Kitaev
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 161, pp. 45–53, 1987.

The author thanks A. R. Its for posing the problem.

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Kitaev, A.V. Method of isomonodromic deformations for “degenerate” third Painlevé equation. J Math Sci 46, 2077–2083 (1989). https://doi.org/10.1007/BF01096090

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  • DOI: https://doi.org/10.1007/BF01096090

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