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arXiv · 2606.18212

Inverse problems for a nonlinear dynamical Schr\"odinger operator with magnetic potential

Mandeep Kumar·Boya Liu·Manmohan Vashisth
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Abstract

We study two inverse problems for a nonlinear dynamical Schr\"odinger equation with time-dependent magnetic and electric potentials. Under suitable analyticity assumptions, we show that the associated Dirichlet-to-Neumann map uniquely determines the linear magnetic potential and all coefficients of the nonlinear electric potential. We establish both full-data and partial-data uniqueness results. For the partial data problem, assuming that the coefficients are known in a neighborhood of the boundary, uniqueness is obtained using measurements made on arbitrarily small open subsets of the boundary. In addition, we establish the well-posedness of the forward problem.

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Mandeep Kumar, Boya Liu, Manmohan Vashisth. 2026-06-16. Inverse problems for a nonlinear dynamical Schr\"odinger operator with magnetic potential. https://arxiv.org/abs/2606.18212

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