Recovery of Schrödinger nonlinearity from the large-data scattering behavior
Yi Sun
Abstract
In this article, we study scattering and inverse scattering problems for 3D nonlinear Schrödinger equations of the form, i∂t u + Δu = a(x)|u|2u. For a(x) in a suitable class, such equations are globally well-posed and admit a large-data scattering theory. In this work, we prove that the large-data scattering behavior uniquely determines the inhomogeneity a(x).
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