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Connections among symmetries, Bäcklund transformation and the Painlevé property for Burger’s hierarchies. (Chinese. English summary) Zbl 0743.35066

Summary: The connections among symmetries, the Bäcklund transformation and the Painlevé property for Burgers hierarchies are discussed. Firstly, the Bäcklund transformation is constructed by means of the symmetries; then according to the symmetries and Bäcklund transformation, the Painlevé property for Burgers hierarchies can be analysed.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
58J72 Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds
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