Symmetries in the fourth Painleve equation and Okamoto polynomials

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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.
25 pages, amslatex

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Quantum Algebra

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http://salesiana.dossiersoluciones.com/handle/123456789/153742

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/q-alg/9708018
 http://arxiv.org/abs/q-alg/9708018

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arXiv