Numerical reconstruction of Schrödinger equations with quadratic nonlinearities

We introduce a numerical framework for reconstructing the potential in two dimensional semilinear elliptic PDEs with power type nonlinearities from the nonlinear Dirichlet to Neumann map. By applying higher order linearization method, we compute the Fourier data of the unknown potential and then invert it to recover $q$. Numerical experiments show accurate reconstructions for both smooth and discontinuous test cases.