Solutions of Adler's Lattice Equation Associated with 2-Cycles of the Bäcklund Transformation

DOI

10.2991/jnmp.2008.15.s3.4How to use a DOI?

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

© 2008, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - James Atkinson
AU  - Frank Nijhoff
PY  - 2008
DA  - 2008/10/01
TI  - Solutions of Adler's Lattice Equation Associated with 2-Cycles of the Bäcklund Transformation
JO  - Journal of Nonlinear Mathematical Physics
SP  - 34
EP  - 42
VL  - 15
IS  - supplement 3
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2008.15.s3.4
DO  - 10.2991/jnmp.2008.15.s3.4
ID  - Atkinson2008
ER  -