On Hamiltonian Formalism for Dressing Chain Equations of Even Periodicity

Abstract

We propose a Hamiltonian formalism for N periodic dressing chain with the even number N. The formalism is based on Dirac reduction applied to the N + 1 periodic dressing chain with the odd number N +1 for which the Hamiltonian formalism is well known. The Hamilton dressing chain equations in the N even case depend explicitly on a pair of conjugated Dirac constraints and are equivalent to A(1)N−1 invariant symmetric Painlevé equations.