Tau-functions and special solutions in a coupled Painlevé system

Abstract

For a pair of coupled Painlevé equations obtained as a similarity reduction of the Hirota-Satsuma systems we describe special parameter-families of solutions given in terms of mixtures of rational and Airy functions, and in terms of a second Painlevé transcendent. The tau-functions associated to some of these solutions are also given explicitly.

Poster from NEEDS 2001, Cambridge