The Weiss-Tabor-Carnevale Painlevé test and Burgers' hierarchy

Andrew Pickering

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)821-833
Number of pages13
JournalJournal of Mathematical Physics
Issue number2
Publication statusPublished - 1994


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