Backlund transformations for the second Painleve hierarchy: a modified truncation approach

The second Painleve hierarchy is defined as the hierarchy of ordinary diffe rential equations obtained by similarity reduction from the modified Kortew eg-de Vries hierarchy. Its first member is the well known second Painleve e quation, P-11. In this paper we use this hierarchy in order to illustrate our application of the truncation procedure in Painleve analysis to ordinary differential e quations. We extend these techniques in order to derive auto-Backlund trans formations for the second Painleve hierarchy. We also derive a number of ot her Backlund transformations, including a Backlund transformation onto a hi erarchy of P-34 equations, and a little known Backlund transformation for P -11 itself. We then use our results on Backlund transformations to obtain, for each mem ber of the P-11 hierarchy, a sequence of special integrals.