  We prove that any gauged WZNW model has a Lax pair representation, and give
explicitly the general solution of the classical equations of motion of the
SL(2,R)/U(1) theory. We calculate the symplectic structure of this solution by
solving a differential equation of the Gelfand-Dikii type with initial state
conditions at infinity, and transform the canonical physical fields non-locally
onto canonical free fields. The results will, finally, be collected in a local
B\"acklund transformation. These calculations prepare the theory for an exact
canonical quantization.
