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

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

2008-06-15

arxiv.org/abs/0806.2431v8

Mathematics

Algebraic Geometry

26 pages, 2 figures

Scientific paper

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 Painlev\'e 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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