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arXiv · 2304.01455

Recovery of the nonlinearity from the modified scattering map

Gong Chen·Jason Murphy
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Abstract

We consider a class of one-dimensional nonlinear Schr\"odinger equations of the form \[ (i\partial_t+\Delta)u = [1+a]|u|^2 u. \] 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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Gong Chen, Jason Murphy. 2023-04-04. Recovery of the nonlinearity from the modified scattering map. https://arxiv.org/abs/2304.01455

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