Inverse fixed energy scattering problem for the generalized nonlinear Schrodinger operator

We consider an inverse fixed energy scattering problem for the generalized nonlinear Schrodinger operator. We prove that in a three-dimensional case, the unknown compactly supported potentials from L-p space can be uniquely obtained by the scattering data with fixed positive energy (by the knowledge of the scattering amplitude with the fixed spectral parameter). The proof is based on the new estimates for the Green-Faddeev function in L-infinity(R-n) space for n = 2 and 3. The results may have applications in nonlinear optics for the saturation model. In particular, the constant coefficients of this model can be uniquely reconstructed by the scattering data with fixed energy.