Rational Solutions of Painlevé Equations

Publisher: John Wiley & Sons Inc

E-ISSN: 1467-9590|61|1|31-53

ISSN: 0022-2526

Source: STUDIES IN APPLIED MATHEMATICS, Vol.61, Iss.1, 1979-07, pp. : 31-53

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Abstract

With Bäcklund transformations, we construct explicit solutions of Painlevé equations 2 and 4. Independently, we find solutions of degenerate cases of equations 3 and 5. The six Painlevé transcendents are referred to as 1–6.