On Hamiltonian Formalism for Dressing Chain Equations of Even Periodicity

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 th...

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Bibliographic Details
Published in:Open Communications in Nonlinear Mathematical Physics 2022-11, Vol.2
Main Authors: Aratyn, H., Gomes, J. F., Zimerman, A. H.
Format: Article
Language:English
Subjects:
mathematical physics
nonlinear sciences - exactly solvable and integrable systems
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Summary: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 Painlev\'e equations.
ISSN:2802-9356
2802-9356
DOI:10.46298/ocnmp.10161