Geodesic
Symmetries and Special Solutions of Reductions of the Lattice Potential KdV Equation
Symmetry, integrability and geometry: methods and applications, Tome 10 (2014) Cet article a éte moissonné depuis la source Math-Net.Ru

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We identify a periodic reduction of the non-autonomous lattice potential Korteweg-de Vries equation with the additive discrete Painlevé equation with $E_6^{(1)}$ symmetry. We present a description of a set of symmetries of the reduced equations and their relations to the symmetries of the discrete Painlevé equation. Finally, we exploit the simple symmetric form of the reduced equations to find rational and hypergeometric solutions of this discrete Painlevé equation.
Keywords: difference equations; integrability; reduction; isomonodromy. 
@article{SIGMA_2014_10_a1,
     author = {Christopher M. Ormerod},
     title = {Symmetries and {Special} {Solutions} of {Reductions} of the {Lattice} {Potential} {KdV} {Equation}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2014},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2014_10_a1/}
}
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Christopher M. Ormerod. Symmetries and Special Solutions of Reductions of the Lattice Potential KdV Equation. Symmetry, integrability and geometry: methods and applications, Tome 10 (2014). http://geodesic.mathdoc.fr/item/SIGMA_2014_10_a1/

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