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arXiv · 0710.2643

Solutions of Adler's lattice equation associated with 2-cycles of the Backlund transformation

James Atkinson·Frank Nijhoff
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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.

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James Atkinson, Frank Nijhoff. 2007-10-14. Solutions of Adler's lattice equation associated with 2-cycles of the Backlund transformation. https://doi.org/10.2991/jnmp.2008.15.s3.4

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