Trace formulas revisited and a new representation of KdV solutions with short-range initial data
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910621762584576 |
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| author | Rybkin, Alexei |
| author_facet | Rybkin, Alexei |
| contents | We put forward a new approach to Deift-Trubowitz type trace formulas for the 1D Schrodinger operator with potentials that are summable with the first moment (short-range potentials). We prove that these formulas are preserved under the KdV flow whereas the class of short-range potentials is not. Finally, we show that our formulas are well-suited to study the dispersive smoothing effect. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_13656 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Trace formulas revisited and a new representation of KdV solutions with short-range initial data Rybkin, Alexei Mathematical Physics Analysis of PDEs We put forward a new approach to Deift-Trubowitz type trace formulas for the 1D Schrodinger operator with potentials that are summable with the first moment (short-range potentials). We prove that these formulas are preserved under the KdV flow whereas the class of short-range potentials is not. Finally, we show that our formulas are well-suited to study the dispersive smoothing effect. |
| title | Trace formulas revisited and a new representation of KdV solutions with short-range initial data |
| topic | Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2308.13656 |