On some Hamiltonian structures of coupled Painlevé II systems in dimension four

Details On some Hamiltonian structures of coupled Painlevé II systems in dimension four On some Hamiltonian structures of coupled Painlevé II systems in dimension four

2007-04-22

arxiv.org/abs/0704.2863v2

Mathematics

Algebraic Geometry

9 pages

Scientific paper

We find and study a two-parameter family of coupled Painlev\'e II systems in dimension four with affine Weyl group symmetry of several types. Moreover, we find a three-parameter family of polynomial Hamiltonian systems in two variables $t,s$. Setting $s=0$, we can obtain an autonomous version of the coupled Painlev\'e II systems. We also show its symmetry and holomorphy conditions.

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