James Atkinson et al 2008 J. Phys. A: Math. Theor. 41 142001 doi:10.1088/1751-8113/41/14/142001
Soliton solutions for Q3
FREE ARTICLEJames Atkinson1, Jarmo Hietarinta2 and Frank Nijhoff1
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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 τ-function of the Hirota–Miwa equation.
- PACS
- MSC
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35Q51 Solitons (See also 37K40)
35Q58 Other completely integrable equations (See also 37J35, 37K10)
15A63 Quadratic and bilinear forms, inner products [See mainly 11Exx]
- Subjects
- Dates
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Issue 14 (11 April 2008)
Received 9 January 2008, in final form 8 February 2008
Published 26 March 2008
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Soliton solutions for Q3
James Atkinson et al 2008 J. Phys. A: Math. Theor. 41 142001
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