Geodesic
Rational Solutions of the H3 and Q1 Models in the ABS Lattice List
Symmetry, integrability and geometry: methods and applications, Tome 7 (2011) Cet article a éte moissonné depuis la source Math-Net.Ru

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In the paper we present rational solutions for the H3 and Q1 models in the Adler–Bobenko–Suris lattice list. These solutions are in Casoratian form and are generated by considering difference equation sets satisfied by the basic Casoratian column vector.
Keywords: Casoratian; bilinear; rational solutions; H3; Q1. 
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     author = {Ying Shi and Da-jun Zhang},
     title = {Rational {Solutions} of the {H3} and {Q1} {Models} in the {ABS} {Lattice} {List}},
     journal = {Symmetry, integrability and geometry: methods and applications},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a45/}
}
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Ying Shi; Da-jun Zhang. Rational Solutions of the H3 and Q1 Models in the ABS Lattice List. Symmetry, integrability and geometry: methods and applications, Tome 7 (2011). http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a45/

[1] Nijhoff F. W., Walker A. J., “The discrete and continuous Painlevé VI hierarchy and the Garnier systems”, Glasgow Math. J., 43:A (2001), 109–123, arXiv: nlin.SI/0001054 | DOI | MR

[2] Adler V. E., Bobenko A. I., Suris Yu. B., “Classification of integrable equations on quad-graphs. The consistency approach”, Comm. Math. Phys., 233 (2003), 513–543, arXiv: nlin.SI/0202024 | DOI | MR | Zbl

[3] Atkinson J., Hietarinta J., Nijhoff F., “Seed and soliton solutions of Adler's lattice equation”, J. Phys. A: Math. Theor., 40 (2007), F1–F8, arXiv: nlin.SI/0609044 | DOI | Zbl

[4] Atkinson J., Hietarinta J., Nijhoff F., “Soliton solutions for Q3”, J. Phys. A: Math. Theor., 41 (2008), 142001, 11 pp., arXiv: 0801.0806 | DOI | MR | Zbl

[5] Nijhoff F., Atkinson J., Hietarinta J., “Soliton solutions for ABS lattice equations. I. Cauchy matrix approach”, J. Phys. A: Math. Theor., 42 (2009), 404005, 34 pp., arXiv: 0902.4873 | DOI | MR | Zbl

[6] Hietarinta J., Zhang D. J., “Soliton solutions for ABS lattice equations. II. Casoratians and bilinearization”, J. Phys. A: Math. Theor., 42 (2009), 404006, 30 pp., arXiv: 0903.1717 | DOI | MR | Zbl

[7] Hietarinta J., Zhang D. J., “Multisoliton solutions to the lattice Boussinesq equation”, J. Math. Phys., 51 (2010), 033505, 12 pp., arXiv: 0906.3955 | DOI | MR

[8] Atkinson J., Nijhoff F., “A constructive approach to the soliton solutions of integrable quadrilateral lattice equations”, Comm. Math. Phys., 299 (2010), 283–304, arXiv: 0911.0458 | DOI | MR | Zbl

[9] Nijhoff F., Atkinson J., “Elliptic $N$-soliton solutions of ABS lattice equations”, Int. Math. Res. Not., 2010:20 (2010), 3837–3895, arXiv: 0911.0461 | DOI | MR | Zbl

[10] Ablowitz M. J., Satsuma J., “Solitons and rational solutions of nonlinear evolution equations”, J. Math. Phys., 19 (1978), 2180–2186 | DOI | MR | Zbl

[11] Zhang D. J., Notes on solutions in Wronskian form to soliton equations: KdV-type, arXiv: nlin.SI/0603008

[12] Zhang D. J., Hietarinta J., “Generalized solutions for the H1 model in ABS list of lattice equations”, Nonlinear and Modern Mathematical Physics (July 15–21, 2009, Beijing), AIP Conf. Proc., 1212, eds. W. X. Ma, X. B. Hu and Q. P. Liu, Amer. Inst. Phys., Melville, NY, 2010, 154–161 | DOI | MR | Zbl

[13] Freeman N. C., Nimmo J. J. C., “Soliton solutions of the Korteweg–de Vries and Kadomtsev–Petviashvili equations: the Wronskian technique”, Phys. Lett. A, 95 (1983), 1–3 | DOI | MR