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We prove that any gauged WZNW model has a Lax pair representation, and giveexplicitly the general solution of the classical equations of motion of theSL(2,R)/U(1) theory. We calculate the symplectic structure of this solution bysolving a differential equation of the Gelfand-Dikii type with initial stateconditions at infinity, and transform the canonical physical fields non-locallyonto canonical free fields. The results will, finally, be collected in a localB\"acklund transformation. These calculations prepare the theory for an exactcanonical quantization.Comment: 20 pages, no figures, LaTeX, uses amsfont

The Complete Solution of the Classical SL(2,ℝ/U(1) Gauged WZNW Field Theory