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Zbl 0865.34010
Kajiwara, Kenji; Ohta, Yasuhiro
Determinant structure of the rational solutions for the Painlevé II equation. (English)
[J] J. Math. Phys. 37, No.9, 4693-4704 (1996). ISSN 0022-2488; ISSN 1089-7658/e

Summary: Two types of determinant representations of the rational solutions for the Painlevé II equation are discussed by using the bilinear formalism. One of them is a representation by the Devisme polynomials, and another one is the Hankel determinant representation. They are derived from the determinant solutions of the KP hierarchy and Toda lattice, respectively.

MSC 2000:: *34A34 Nonlinear ODE and systems, general
35Q53 KdV-like equations

Keywords: rational solutions; Painlevé II equation; bilinear formalism; determinant solutions

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