An inverse Born approximation for the general nonlinear Schrodinger operator on the line

This work deals with the inverse scattering problems for the one-dimensional Schrodinger equation of the most general form -u '' + F(x, u) = k(2)u, with general nonlinearity F and with a real parameter k. Under some assumptions on F we prove that all singularities and jumps of F(x, u(0)), where u(0)(x, k) = e(ikx), can be recovered by the reflection coefficient with arbitrary large k.