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We consider the scattering transform for the first order system in the plane,  (D-Q) \psi =0 where D is the 2x2 diagonal matrix differential operator whosediagonal entries are d-bar and d and Q is a 2x2 off-diagonal matrix. We showthat the scattering map is Lipschitz continuous on a neighborhood of zero inL^2.Comment: 13 pages, 14 references, no figures v2. corrects typoes and improves  the expositio

Estimates for the Scattering Map Associated with a Two-Dimensional First-Order System