title: |
Solutions of Adler's Lattice Equation Associated with 2-Cycles of the Bäcklund Transformation |
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publication: |
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| 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 |
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publication date: |
October 2008 |
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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. |
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copyright: |
©
Atlantis Press. This article is distributed under the
terms of the Creative Commons Attribution License, which permits
non-commercial use, distribution and reproduction in any medium,
provided the original work is properly cited. |
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full text: |