Seed and soliton solutions for Adler's lattice equation

James Atkinson; Jarmo Hietarinta; Frank Nijhoff

doi:10.1088/1751-8113/40/1/f01

Seed and soliton solutions for Adler's lattice equation

James Atkinson, Jarmo Hietarinta, Frank Nijhoff

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38 Citations (Scopus)

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.

Original language	English
Pages (from-to)	F1-F8
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	40
Issue number	1
DOIs	https://doi.org/10.1088/1751-8113/40/1/f01
Publication status	Published - 2006

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title = "Seed and soliton solutions for Adler's lattice equation",

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 B{\"a}cklund 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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AU - Hietarinta, Jarmo

AU - Nijhoff, Frank

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AB - 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.

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DO - 10.1088/1751-8113/40/1/f01

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SP - F1-F8

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

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Seed and soliton solutions for Adler's lattice equation

Abstract

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