iv : 0 80 1 . 08 06 v 1 [ nl in . S I ] 7 J an 2 00 8 Soliton solutions for Q 3
نویسندگان
چکیده
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 Bäcklund 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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