Special polynomials and the Hirota Bilinear relations of the second and the fourth Painleve equations

Authors
Fukutani, S Okamoto, K Umemura, H
Citation
S. Fukutani et al., Special polynomials and the Hirota Bilinear relations of the second and the fourth Painleve equations, NAG MATH J, 159, 2000, pp. 179-200
Citations number
7
Categorie Soggetti
Mathematics
Journal title
NAGOYA MATHEMATICAL JOURNAL
ISSN journal
00277630 → ACNP
Volume
159
Year of publication
2000
Pages
179 - 200
Database
ISI
SICI code
0027-7630(200009)159:<179:SPATHB>2.0.ZU;2-T
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.