Geodesic
Integrable hierarchies: Painlev\'e indices and compatibility conditions
Teoretičeskaâ i matematičeskaâ fizika, Tome 99 (1994) no. 3, pp. 509-516

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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. 
@article{TMF_1994_99_3_a20,
     author = {A. Pickering},
     title = {Integrable hierarchies: {Painlev\'e} indices and compatibility conditions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {509--516},
     publisher = {mathdoc},
     volume = {99},
     number = {3},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1994_99_3_a20/}
}
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A. Pickering. Integrable hierarchies: Painlev\'e 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/