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arXiv · 0801.0806

Soliton solutions for Q3

James Atkinson·Jarmo Hietarinta·Frank Nijhoff
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Abstract

We construct N-soliton solutions to the equation called Q3 in the recent Adler-Bobenko-Suris classification. An essential ingredient in the construction is the relationship of $(Q3)_{\delta=0}$ to the equation proposed by Nijhoff, Quispel and Capel in 1983 (the NQC equation). This latter equation has two extra parameters, and depending on their sign choices we get a 4-to-1 relationship from NQC to $(Q3)_{\delta=0}$. This leads to a four-term background solution, and then to a 1-soliton solution using a Backlund transformation. Using the 1SS as a guide allows us to get the N-soliton solution in terms of the tau-function of the Hirota-Miwa equation.

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James Atkinson, Jarmo Hietarinta, Frank Nijhoff. 2008-01-07. Soliton solutions for Q3. https://doi.org/10.1088/1751-8113/41/14/142001

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