Soliton solutions for Q3

2008/01/07 by James Atkinson, Jarmo Hietarinta, Frank Nijhoff · 2 citations
Physics and Astronomy · #nlin.SI

paper · pdf · doi:10.1088/1751-8113/41/14/142001

published as J. Phys. A: Math. Theor. 41 (2008) 142001 · 11 pages

arxiv created 2008/01/07 · arxiv updated 2011/05/27

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)_δ=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)_δ=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.

Cited by

• Discrete Gerdjikov-Ivanov models and their higher-order counterparts from the Cauchy matrix scheme
• On consistency around a 3 × 3× 3 cube and Q3 analogue of the lattice Boussinesq equation

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