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

Summary

We consider the scattering transform for the first-order system in the plane,

$$\left( {\begin{array}{*{20}c} {\partial _{\bar x} } & 0 \\ 0 & {\partial _x } \\ \end{array} } \right)\psi - \left( {\begin{array}{*{20}c} 0 & {q^1 } \\ {q^2 } & 0 \\ \end{array} } \right)\psi = 0.$$

We show that the scattering map is Lipschitz continuous on a neighborhood of zero in L ².