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The Weiss-Tabor-Carnevale Painlevé test and Burgers’ hierarchy. (English) Zbl 0811.35130
Summary: The Weiss-Tabor-Carnevals (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 Burger’s 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.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
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References:
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