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title:
 
Solutions of Adler's Lattice Equation Associated with 2-Cycles of the Bäcklund Transformation
publication:
 
JNMP
volume-issue:   15 - supplement 3
pages:   34 - 42
ISSN:
  1402-9251
DOI:
  doi:10.2991/jnmp.2008.15.s3.4 (how to use a DOI)
author(s):
 
James Atkinson, Frank Nijhoff
publication date:
 
October 2008
abstract:
 
The Bäcklund transformation (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 Bäcklund 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 associated with 2-cycles of the BT.
copyright:
 
© The authors.
This article is distributed under the terms of the Creative Commons Attribution License 4.0, which permits non-commercial use, distribution and reproduction in any medium, provided the original work is properly cited. See for details: https://creativecommons.org/licenses/by-nc/4.0/
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