W--Gravity and Generalized Lax Equations for (super) Toda Theory
  We generalize the Lax pair and B\"acklund transformations for Toda and N=1 super Toda equations to the case of arbitrary worldsheet background geometry. We use the fact that the Toda equations express constant curvature conditions, which arise naturally from flatness conditions equivalent to the W--gravity equations of motion. 
Kenichro Aoki and Eric D'Hoker