On B\"{a}cklund transformations and boundary conditions associated with the quantum inverse problem for a discrete nonlinear integrable system and its connection to Baxter's Q-operator
Abstract
A discrete nonlinear system is analysed in case of open chain boundary conditions at the ends. It is shown that the integrability of the system remains intact, by obtaining a modified set of Lax equations which automatically take care of the boundary conditions. The same Lax pair also conforms to the conditions stipulated by Sklyanin [5]. The quantum inverse problem is set up and the diagonalisation is carried out by the method of sparation of variables. B\"{a}cklund transformations are then derived under the modified boundary conditions using the classical r-matrix . Finally by quantising the B\"{a}cklund transformation it is possible to identify the relation satisfied by the eigenvalue of Baxter's Q-operator even for the quasi periodic situation.
Keywords
Cite
@article{arxiv.math-ph/0202027,
title = {On B\"{a}cklund transformations and boundary conditions associated with the quantum inverse problem for a discrete nonlinear integrable system and its connection to Baxter's Q-operator},
author = {A. Ghose Choudhury and A. Roy Chowdhury},
journal= {arXiv preprint arXiv:math-ph/0202027},
year = {2007}
}