Seed and soliton solutions for Adler's lattice equation
Exactly Solvable and Integrable Systems
2007-05-23 v1
Abstract
Adler's lattice equation has acquired the status of a master equation among 2D discrete integrable systems. In this paper we derive what we believe are the first explicit solutions of this equation. In particular it turns out necessary to establish a non-trivial seed solution from which soliton solutions can subsequently be constructed using the B\"acklund transformation. As a corollary we find the corresponding solutions of the Krichever-Novikov equation which is obtained from Adler's equation in a continuum limit.
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@article{arxiv.nlin/0609044,
title = {Seed and soliton solutions for Adler's lattice equation},
author = {James Atkinson and Jarmo Hietarinta and Frank Nijhoff},
journal= {arXiv preprint arXiv:nlin/0609044},
year = {2007}
}
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9 pages pdf file