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 $A_{N-1}^{(1)}$ invariant symmetric Painlevé equations.

arXiv comment13 pages, comment added in subsection 3.1

References in corpus (8)

• Affine Weyl groups, discrete dynamical systems and Painleve equations
• Painleve equations from Darboux chains - Part 1: P3-P5
• Spectral curve, Darboux coordinates and Hamiltonian structure of periodic dressing chains
• From bi-Hamiltonian geometry to separation of variables: stationary Harry-Dym and the KdV dressing chain
• Bäcklund Transformations of MKdV and Painlevé Equations
• A Symmetric System of Mixed Painleve III - V Equations and its Integrable Origin
• Gauge Symmetry Origin of Bäcklund Transformations for Painlevé Equations
• A symmetry reduction technique for higher order Painlevé systems

Cited by in corpus (2)

• On Rational Solutions of Dressing Chains of Even Periodicity
• Extended symmetry of higher Painlevé equations of even periodicity and their rational solutions