Numerical reconstruction of Schrödinger equations with quadratic nonlinearities
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909968659120128 |
|---|---|
| author | Maddah, Khaoula El Lassas, Matti Tyni, Teemu |
| author_facet | Maddah, Khaoula El Lassas, Matti Tyni, Teemu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16269 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Numerical reconstruction of Schrödinger equations with quadratic nonlinearities Maddah, Khaoula El Lassas, Matti Tyni, Teemu Numerical Analysis Analysis of PDEs 65N21, 35R30, 35J61 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. |
| title | Numerical reconstruction of Schrödinger equations with quadratic nonlinearities |
| topic | Numerical Analysis Analysis of PDEs 65N21, 35R30, 35J61 |
| url | https://arxiv.org/abs/2512.16269 |