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On a General Singular Solution of the Fifth Painlevé Equation Along the Positive Real Axis

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Abstract

We propose a system of non-linear equations equivalent to the fifth Painlevé equation, which enables us to examine the general singular solution given by Andreev and Kitaev along the positive real axis. We present a two-parameter family of asymptotic solutions corresponding to this general singular solution, and pose a conjecture.

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Authors and Affiliations

  1. Department of Mathematics, Keio University, 3-14-1, Hiyoshi, Kohoku-ku, Yokohama, 223-8522, Japan

    Shun Shimomura

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  1. Shun Shimomura
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Correspondence to Shun Shimomura.

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Communicated by Aimo Hinkkanen.

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Shimomura, S. On a General Singular Solution of the Fifth Painlevé Equation Along the Positive Real Axis. Comput. Methods Funct. Theory 21, 633–651 (2021). https://doi.org/10.1007/s40315-021-00391-8

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  • DOI: https://doi.org/10.1007/s40315-021-00391-8

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