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We show that the knowledge of the Dirichlet--to--Neumann map for a nonlinearmagnetic Schr\"odinger operator on the boundary of a compact complex manifold,equipped with a K\"ahler metric and admitting sufficiently many globalholomorphic functions, determines the nonlinear magnetic and electricpotentials uniquely.

A remark on inverse problems for nonlinear magnetic Schr\"odinger equations on complex manifolds