Applied Mathematics Seminar

There has recently been a great deal of interest in deriving higher order analogues of the well known six Painleve' equations. There then also arises the fundamental question of the derivation of transformation properties (also known as Backlund transformations) for such higher order equations.

In this seminar we derive Backlund transformations for every member of a recently obtained fourth Painleve' hierarchy. The relationship of some of these Backlund transformations to known Miura transformations is also explained.