Year: 2025
Type: preprint
Abstract: In this work, we address an inverse problem for a defocusing cubic nonlinear Schr\"{o}dinger (NLS) equation in dimensions $d\in\{1, 2,3\}$ in a range of Sobolev spaces $H^s(\mathbb{R}^d)$ by employing the method of approximate solutions. We recover a smooth, space-dependent and compactly supported function $\alpha$ that controls the nonlinearity (and thus self-interaction strength) in a multiplicative fashion. To the best of our knowledge, this is the first work based on approximate solutions in Sobolev spaces that treats an inverse problem for the NLS and provides explicit recovery of $\alpha$.
Source: arXiv (Cornell University)
Authors: Lee, Zachary, Pavlovi\'c, Nata\v{s}a
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979280362
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