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The Hamiltonian Structure of the Second Painleve Hierarchy

Marta Mazzocco·Man Yue Mo
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Abstract

In this paper we study the Hamiltonian structure of the second Painleve hierarchy, an infinite sequence of nonlinear ordinary differential equations containing PII as its simplest equation. The n-th element of the hierarchy is a non linear ODE of order 2n in the independent variable $z$ depending on n parameters denoted by ${t}_1,...,{t}_{n-1}$ and $α_n$. We introduce new canonical coordinates and obtain Hamiltonians for the $z$ and $t_1,...,t_{n-1}$ evolutions. We give explicit formulae for these Hamiltonians showing that they are polynomials in our canonical coordinates.

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Marta Mazzocco, Man Yue Mo. 2006-10-27. The Hamiltonian Structure of the Second Painleve Hierarchy. https://doi.org/10.1088/0951-7715%2F20%2F12%2F006

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