Numerical reconstruction of Schrödinger equations with quadratic nonlinearities
Abstract
Abstract 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.
Fields of Study & Subjects
Numerical methods in inverse problems
Advanced Mathematical Physics Problems
Mathematical Analysis and Transform Methods
Publication details
- Journal / source
- Inverse Problems
- Volume
- 42
- Issue
- 9
- Pages
- 095011–095011
- Publication date
- 4 September 2026