On the properties of Bäcklund transformations on Painleväé 6th equations
DOI:
https://doi.org/10.5564/jasea.v4i1.3222Keywords:
Painlevé equations , Bäcklund transformations, Affine Weyl group, Bonnet surfacesAbstract
In his series of papers Okamoto give detailed explanation of Painlevé equations of types 2-6. On the other hand Kajiwara et.al described Bäcklund transformations for these types of Painlevé equations. Later, Bobenko and Eitner found that Painlevé equations of types 6 and 5 give rise Bonnet surfaces and vise-versa. In this research we study properties of Bäcklund transformations of 6th Painlevé equations P6 and determine explicit formula of such transformations which give a new Bonnet surfaces.
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A. Bobenko and U.Eitner, Painlevé equations in the differential geometry, Lecture notes in mathematics, 1753, (2000). https://doi.org/10.1007/b76883
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