## Birational Symmetries, Hirota Bilinear Forms and Special Solutions of the Garnier Systems in 2-variables

J. Math. Sci. Univ. Tokyo
Vol. 10 (2003), No. 2, Page 355--371.

Tsuda, Teruhisa
Birational Symmetries, Hirota Bilinear Forms and Special Solutions of the Garnier Systems in 2-variables
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Abstract:
Hirota bilinear forms of the Garnier system in 2-vari\-ables, $G(1,1,1,1,1)$, are given. By using Hirota bilinear forms we construct new birational symmetries of $G(1,1,1,1,1)$. We obtain special solutions of the Garnier system in $n$-variables, which are described in terms of solutions of the Garnier system in $(n-1)$-variables. We investigate also algebraic solutions for $n=2$.

Mathematics Subject Classification (2000): Primary 34M55; Secondary 33E17
Mathematical Reviews Number: MR1987136

Received: 2002-05-27