Nagoya Mathematical Journal

Special polynomials and the Hirota bilinear relations of the second and the fourth Painlevé equations

Satoshi Fukutani, Kazuo Okamoto, and Hiroshi Umemura

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Abstract

We give a purely algebraic proof that the rational functions $P_n(t),\, Q_n(t)$ inductively defined by the recurrence relation (1), (2) respectively, are polynomials. The proof reveals the Hirota bilinear relations satisfied by the $\tau$-functions.

Article information

Source
Nagoya Math. J., Volume 159 (2000), 179-200.

Dates
First available in Project Euclid: 27 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1114631457

Mathematical Reviews number (MathSciNet)
MR1783569

Zentralblatt MATH identifier
0972.34077

Subjects
Primary: 34M55: Painlevé and other special equations; classification, hierarchies;
Secondary: 33E17 37K10: Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)

Citation

Fukutani, Satoshi; Okamoto, Kazuo; Umemura, Hiroshi. Special polynomials and the Hirota bilinear relations of the second and the fourth Painlevé equations. Nagoya Math. J. 159 (2000), 179--200. https://projecteuclid.org/euclid.nmj/1114631457


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References

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