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Special Solutions of the Sixth Painleve Equation with Solvable Monodromy

2006/10/23 by Kazuo Kaneko, Kaneko, Kazuo, Shoji Okumura +1
Mathematics · Physics and Astronomy · #33E17 #34M55 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Waves and Solitons #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.math/0610673

openalex publication_date 2006/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We will study two types of special solutions of the sixth Painleve equation, which are invariant under the symmetries obtained from the Backlund transformations. In most cases, the fixed points of the Backlund transformations are classical solution, but our solutions are not classical for generic parameters. We will calculate the linear monodromy of these solutions exactly, and we will characterize them on Fricke's cubic surface of monodromy.

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