Volume 15, Issue supplement 3, October 2008, Pages 34 - 42
Solutions of Adler's Lattice Equation Associated with 2-Cycles of the Bäcklund Transformation
James Atkinson, Frank Nijhoff
Available Online 1 October 2008.
- https://doi.org/10.2991/jnmp.2008.15.s3.4How to use a DOI?
- 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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Cite this article
TY - JOUR AU - James Atkinson AU - Frank Nijhoff PY - 2008 DA - 2008/10 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 - https://doi.org/10.2991/jnmp.2008.15.s3.4 ID - Atkinson2008 ER -