Solutions of Adler's lattice equation associated with 2-cycles of the Backlund transformation
arXiv:0710.2643 · doi:10.2991/jnmp.2008.15.s3.4
Abstract
The BT of Adler's lattice equation is inherent in the equation itself by virtue of its multidimensional consistency. We refer to a solution of the equation that is related to itself by the composition of two BTs (with different Backlund parameters) as a 2-cycle of the BT. In this article we will show that such solutions are associated with a commuting one-parameter family of rank-2 (i.e., 2-variable), 2-valued mappings. We will construct the explicit solution of the mappings within this family and hence give the solutions of Adler's equation that are 2-cycles of the BT.
10 pages, contribution to the NEEDS 2007 proceedings