Backlund Transformations for Darboux Integrable Differential Systems
  We give a new mechanism for constructing Backlund transformations by using symmetry reduction of differential systems. We then characterize a family of Backlund transformations between Darboux integrable systems where the Backlund transformation can be constructed by the proposed symmetry reduction method. 
Ian M. Anderson, Mark E. Fels
math.DG