Thoughts about potentials with finite-band spectrum and finite-dimensional reductions of integrable systems
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| Format: | Preprint |
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2024
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| _version_ | 1866915372749291520 |
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| author | Konyaev, Andrey Yu. Matveev, Vladimir S. |
| author_facet | Konyaev, Andrey Yu. Matveev, Vladimir S. |
| contents | We repeat, using methods developed for BKM systems, the famous results of S. Novikov (1974), J. Moser (1981, 1982) , and A. Veselov (1980) that relate Schrödinger-Hill operators with finite-band spectra, solutions of the Neumann system, and certain solutions of the KdV equations. Our general motivation is to determine whether it is possible to apply inverse scattering methods to BKM systems, and in the conclusion, we indicate initial observations in this direction. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_02290 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Thoughts about potentials with finite-band spectrum and finite-dimensional reductions of integrable systems Konyaev, Andrey Yu. Matveev, Vladimir S. Mathematical Physics Differential Geometry Exactly Solvable and Integrable Systems We repeat, using methods developed for BKM systems, the famous results of S. Novikov (1974), J. Moser (1981, 1982) , and A. Veselov (1980) that relate Schrödinger-Hill operators with finite-band spectra, solutions of the Neumann system, and certain solutions of the KdV equations. Our general motivation is to determine whether it is possible to apply inverse scattering methods to BKM systems, and in the conclusion, we indicate initial observations in this direction. |
| title | Thoughts about potentials with finite-band spectrum and finite-dimensional reductions of integrable systems |
| topic | Mathematical Physics Differential Geometry Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2411.02290 |