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.
An inverse problem for the Schr¨ odinger equation with Neumann boundary condition.Advances in Pure and Applied Mathematics, 14(1):50–69
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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.