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arXiv · 2606.14458

An Inverse problem for a fourth order nonlinear Schr\"odinger equation (NLS)

Rohit Kumar Mishra·Anamika Purohit·Suman Kumar Sahoo
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Abstract

We study an inverse problem for the time-dependent nonlinear fourth-order Schr\"odinger equation on both compact Euclidean domains and compact Riemannian manifolds, (say) $M$. This model arises in nonlinear fiber optics and the theory of optical solitons in gyrotropic media. Our main objective is the identification of unknown coefficients from the associated source-to-solution map, which assigns to each source term $f$, supported in $(0, T)\times \Gamma$, the corresponding solution $u$ restricted to the same set, where $\Gamma \subset M$ is a neighborhood of $\partial M$. We prove that the zeroth-order term, the second-order coefficient, and the nonlinear coefficient are uniquely determined by this map. Moreover, the recovery of the symmetric second-order tensor reduces to the inversion of a divergent beam transform.

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Rohit Kumar Mishra, Anamika Purohit, Suman Kumar Sahoo. 2026-06-12. An Inverse problem for a fourth order nonlinear Schr\"odinger equation (NLS). https://arxiv.org/abs/2606.14458

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