Toda equation and special polynomials associated with the Garnier system

Details Toda equation and special polynomials associated with the Garnier system Toda equation and special polynomials associated with the Garnier system

2004-08-31

arxiv.org/abs/nlin/0408060v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

26 pages

Scientific paper

We prove that a certain sequence of tau functions of the Garnier system
satisfies Toda equation. We construct a class of algebraic solutions of the
system by the use of Toda equation; then show that the associated tau functions
are expressed in terms of the universal character, which is a generalization of
Schur polynomial attached to a pair of partitions.

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