The DBAR Problem and the Thirring Model

We study the Thirring model by means of a DBAR-Riemann-Hilbert problem. We undertake a rigorous study for both the direct and the inverse problem on the class of rapidly decaying potentials. This study includes a discussion of the existence and uniqueness of solutions of the direct and inverse problems, a characterization of the solutions, and an explicit expression for the scattering data in terms of initial scattering functions.