Inverse scattering problem for a cubic string having the shape of a step
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912576192905216 |
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| author | Zolotarev, Vladimir A. |
| author_facet | Zolotarev, Vladimir A. |
| contents | Problem for a cubic string having the shape of a step is studied. It is proved that here we have two scattering problems: the direct one and its dual. The direct problem describes scattering of the waves coming from ``$+\infty$'', and its dual, correspondingly, of the waves from ``$-\infty$''. The main systems of linear singular equations for both problems are obtained. It is shown how to unambiguously restore potential from the solutions to these equation systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_06417 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inverse scattering problem for a cubic string having the shape of a step Zolotarev, Vladimir A. Classical Analysis and ODEs Problem for a cubic string having the shape of a step is studied. It is proved that here we have two scattering problems: the direct one and its dual. The direct problem describes scattering of the waves coming from ``$+\infty$'', and its dual, correspondingly, of the waves from ``$-\infty$''. The main systems of linear singular equations for both problems are obtained. It is shown how to unambiguously restore potential from the solutions to these equation systems. |
| title | Inverse scattering problem for a cubic string having the shape of a step |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2509.06417 |