Symmetries in the fourth Painleve equation and Okamoto polynomials

Masatoshi Noumi; Yasuhiko Yamada

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arXiv · q-alg/9708018

Symmetries in the fourth Painleve equation and Okamoto polynomials

Masatoshi Noumi·Yasuhiko Yamada

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Abstract

We propose a new representation of the fourth Painlevé equation in which the $A^{(1)}_2$-symmetries become clearly visible. By means of this representation, we clarify the internal relation between the fourth Painlevé equation and the modified KP hierarchy. We obtain in particular a complete description of the rational solutions of the fourth Painlevé equation in terms of Schur functions. This implies that the so-called Okamoto polynomials, which arise from the $τ$-functions for rational solutions, are in fact expressible by the 3-reduced Schur functions.

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BibTeX RIS

Masatoshi Noumi, Yasuhiko Yamada. 1997-08-19. Symmetries in the fourth Painleve equation and Okamoto polynomials. https://arxiv.org/abs/q-alg/9708018

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