Rational Solutions of the Painleve' VI Equation

Details Rational Solutions of the Painleve' VI Equation Rational Solutions of the Painleve' VI Equation

2000-07-24

arxiv.org/abs/nlin/0007036v2

J. Phys. A: Math. Gen. 34 (2001) 2281-2294

Nonlinear Sciences

Exactly Solvable and Integrable Systems

13 pages, 1 Postscript figure Typos fixed

Scientific paper

10.1088/0305-4470/34/11/320

In this paper, we classify all values of the parameters $\alpha$, $\beta$,
$\gamma$ and $\delta$ of the Painlev\'e VI equation such that there are
rational solutions. We give a formula for them up to the birational canonical
transformations and the symmetries of the Painlev\'e VI equation.

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