The Weiss-Tabor-Carnevale (WTC) Painlevé test, and its recent perturbative extension, provide necessary conditions for a partial differential equation to have the Painlevé property. It follows that Burgers' hierarchy must pass the WTC Painlevé test. The aim here is to prove this explicitly. In addition the Bäcklund transformation for Burgers' equation, obtained by WTC via truncation, is extended to the entire hierarchy. The recursion operator is found to be related to a simple first order system. © 1994 American Institute of Physics.
|Number of pages
|Journal of Mathematical Physics
|Published - 1994