Polynomial Hamiltonian system in two variables with $W(A_1^{(1)})$-symmetry and the second Painlevé hierarchy

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.

29 pages, 2 figures

References in corpus (1)

• Symmetry and holomorphy of the third-order ordinary differential equation satisfied by the third Painlevé Hamiltonian

Cited by in corpus (2)

• Coupled Painlevé VI systems in dimension four with affine Weyl group symmetry of type $D_6^{(1)}$, II
• Fourth-order ordinary differential equation obtained by similarity reduction of the modifed Sawada-Kotera equation