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Darboux and Binary Darboux Transformations for Discrete Integrable Systems. II. Discrete Potential mKdV Equation
Symmetry, integrability and geometry: methods and applications, Tome 13 (2017) Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper presents two results. First it is shown how the discrete potential modified KdV equation and its Lax pairs in matrix form arise from the Hirota–Miwa equation by a 2-periodic reduction. Then Darboux transformations and binary Darboux transformations are derived for the discrete potential modified KdV equation and it is shown how these may be used to construct exact solutions.
Keywords: partial difference equations; integrability; reduction; Darboux transformation. 
@article{SIGMA_2017_13_a35,
     author = {Ying Shi and Jonathan Nimmo and Junxiao Zhao},
     title = {Darboux and {Binary} {Darboux} {Transformations} for {Discrete} {Integrable} {Systems.} {II.~Discrete} {Potential} {mKdV} {Equation}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2017},
     volume = {13},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2017_13_a35/}
}
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Ying Shi; Jonathan Nimmo; Junxiao Zhao. Darboux and Binary Darboux Transformations for Discrete Integrable Systems. II. Discrete Potential mKdV Equation. Symmetry, integrability and geometry: methods and applications, Tome 13 (2017). http://geodesic.mathdoc.fr/item/SIGMA_2017_13_a35/

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