Bäcklund transformations for the second Painlevé hierarchy: a modified truncation approach

  title={B{\"a}cklund transformations for the second Painlev{\'e} hierarchy: a modified truncation approach},
  author={Peter A. Clarkson and Nalini T. Joshi and Andrew Pickering},
  journal={Inverse Problems},
The second Painlev? hierarchy is defined as the hierarchy of ordinary differential equations obtained by similarity reduction from the modified Korteweg-de Vries hierarchy. Its first member is the well known second Painlev? equation, . In this paper we use this hierarchy in order to illustrate our application of the truncation procedure in Painlev? analysis to ordinary differential equations. We extend these techniques in order to derive auto-B?cklund transformations for the second Painlev… 

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