Integrability aspects of a Schwarzian PDE

We present a reduction of the anti-self-dual Yang-Mills (ASDYM) equations t o a system of partial differential equations (PDEs) introduced recently by Nijhoff et al. (Phys. Lett. A 267 (2000) 147). An auto-Backlund transformat ion of the reduced system is also presented. The system under consideration is related to a fourth-order nonlinear PDE of the Schwarzian type. The sym metry group of the latter equation is calculated and similarity reductions to the Schwarzian equation and the full Painleve III, V and VI are presente d. (C) 2001 Elsevier Science B.V. All rights reserved.