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arXiv · 2208.06047

Recovery of a cubic nonlinearity for the nonlinear Schr\"odinger equation

Christopher C. Hogan·Jason Murphy·David Grow
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Abstract

We consider the problem of recovering a spatially-localized cubic nonlinearity in a nonlinear Schr\"odinger equation in dimensions two and three. We prove that solutions with data given by small-amplitude wave packets accrue a nonlinear phase that determines the X-ray transform of the nonlinear coefficient.

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Christopher C. Hogan, Jason Murphy, David Grow. 2022-08-11. Recovery of a cubic nonlinearity for the nonlinear Schr\"odinger equation. https://arxiv.org/abs/2208.06047

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