A method combining Legendre basis reduction in time with a Carleman-estimate-based contraction mapping reconstructs initial data for nonlinear Schrödinger equations from boundary observations, with proven stability under noise.
Inverse problems for nonlinear magnetic Schr¨ odinger equations on conformally transversally anisotropic manifolds.Analysis and PDE, 16(8):1825–1868
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Inverse initial data for nonlinear Schr\"odinger equation via Carleman estimates and the contraction principle
A method combining Legendre basis reduction in time with a Carleman-estimate-based contraction mapping reconstructs initial data for nonlinear Schrödinger equations from boundary observations, with proven stability under noise.