Geodesic
Integrable hierarchies: Painlevé indices and compatibility conditions
Teoretičeskaâ i matematičeskaâ fizika, Tome 99 (1994) no. 3, pp. 509-516 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the application of the Weiss–Tabor–Carnevale (WTC) Painlevé test to hierarchies of completely integrable evolution equations. A method of constructing the Painlevé index polynomial for such hierarchies is illustrated. For Burgers' hierarchy we are able to show that all WTC compatibility conditions are satisfied. This allows a simple construction of the Painlevé-Bäcklund transformation obtained from truncation of the principal Painlevé expansion. 
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A. Pickering. Integrable hierarchies: Painlevé indices and compatibility conditions. Teoretičeskaâ i matematičeskaâ fizika, Tome 99 (1994) no. 3, pp. 509-516. http://geodesic.mathdoc.fr/item/TMF_1994_99_3_a20/

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