Seed and soliton solutions for Adler's lattice equation

Atkinson, James, Hietarinta, Jarmo and Nijhoff, Frank (2006) Seed and soliton solutions for Adler's lattice equation. Journal of Physics A: Mathematical and Theoretical, 40 (1). F1-F8. ISSN 1751-8113

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Official URL: http://dx.doi.org/10.1088/1751-8113/40/1/f01

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 to be necessary to establish a non-trivial seed solution from which soliton solutions can subsequently be constructed using the Bäcklund 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.

Item Type: Article
Subjects: G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: James Atkinson
Date Deposited: 27 Jan 2014 12:14
Last Modified: 03 Nov 2016 11:33
URI: http://nrl.northumbria.ac.uk/id/eprint/15259

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