The complete solution of the classical \(\text{SL}(2,\mathbb{R})/\text{U}(1)\) gauged WZNW field theory (Q1809233)

The presence of the Lax pair representation for any gauged WZNW model is established. An explicit general solution of the classical equations of motion of the \(SL(2,\mathbb{R})/ U(1)\) theory is given. Its symplectic structure is calculated by solving an initial state problem of a Gelfand-Dikii type equation. On this basis the authors derive a nonlocal canonical free-field transformation of the nonlinear fields of the theory and collect these transformations in a local Bäcklund transformation. The calculations are done for a field-theoretic situation with asymptotic boundary conditions.