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  1. Abstract We consider a class of one-dimensional nonlinear Schrödinger equations of the form $$ \begin{align*} & (i\partial_{t}+\Delta)u = [1+a]|u|^{2} u. \end{align*}$$For suitable localized functions $$a$$, such equations admit a small-data modified scattering theory, which incorporates the standard logarithmic phase correction. In this work, we prove that the small-data modified scattering behavior uniquely determines the inhomogeneity $$a$$. 
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