Geodesic
On non-isospectral flows, Painlev\'e equations, and symmetries of differential and difference equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 93 (1992) no. 3, pp. 473-480

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We identify the Painlevé Lax pairs with those corresponding to stationary solutions of non-isospectral flows, both for partial differential equations and differential-difference equations. We discuss symmetry reductions of integrable differential-difference equations and show that, in contrast with the continuous case, where Painlevé equations naturally arise, in the discrete case the so-called “discrete Painlevé equations” cannot be obtained in this way. Actually, symmetry reductions of integrable differential-difference equations naturally provide “delay Painlevé equations”. 
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     author = {D. Levi and O. Ragnisco and M. A. Rodriguez},
     title = {On non-isospectral flows, {Painlev\'e} equations, and symmetries of differential and difference equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     volume = {93},
     number = {3},
     year = {1992},
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D. Levi; O. Ragnisco; M. A. Rodriguez. On non-isospectral flows, Painlev\'e equations, and symmetries of differential and difference equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 93 (1992) no. 3, pp. 473-480. http://geodesic.mathdoc.fr/item/TMF_1992_93_3_a5/