Wave scattering in 1D: D'Alembert-type representations and a reconstruction method
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912286524833792 |
|---|---|
| author | Kalimeris, Konstantinos Mindrinos, Leonidas |
| author_facet | Kalimeris, Konstantinos Mindrinos, Leonidas |
| contents | We derive the extension of the classical d'Alembert formula for the wave equation, which provides the analytical solution for the direct scattering problem for a medium with constant refractive index; this is achieved by employing results obtained via the Fokas method. This methodology is further extended to a medium with piecewise constant refractive index, providing the apparatus for the solution of the associated inverse scattering problem. Hence, we provide an exact reconstruction method which is valid for both full and phaseless data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_05773 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Wave scattering in 1D: D'Alembert-type representations and a reconstruction method Kalimeris, Konstantinos Mindrinos, Leonidas Analysis of PDEs We derive the extension of the classical d'Alembert formula for the wave equation, which provides the analytical solution for the direct scattering problem for a medium with constant refractive index; this is achieved by employing results obtained via the Fokas method. This methodology is further extended to a medium with piecewise constant refractive index, providing the apparatus for the solution of the associated inverse scattering problem. Hence, we provide an exact reconstruction method which is valid for both full and phaseless data. |
| title | Wave scattering in 1D: D'Alembert-type representations and a reconstruction method |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2307.05773 |