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arXiv · 0806.2431

Polynomial Hamiltonian system in two variables with $W({A}^{(1)}_1)$-symmetry and the second Painlevé hierarchy

Yusuke Sasano
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Abstract

We find a one-parameter family of polynomial Hamiltonian system in two variables with $W({A}^{(1)}_1)$-symmetry. We also show that this system can be obtained by the compatibility conditions for the linear differential equations in three variables. We give a relation between it and the second member of the second Painlevé hierarchy. Moreover, we give some relations between an autonomous version of its polynomial Hamiltonian system in two variables and the mKdV hierarchies.

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Yusuke Sasano. 2012-08-07. Polynomial Hamiltonian system in two variables with $W({A}^{(1)}_1)$-symmetry and the second Painlevé hierarchy. https://arxiv.org/abs/0806.2431

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