Inverse problem for the divisor of the good Boussinesq equation
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914245541625856 |
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| author | Badanin, Andrey Korotyaev, Evgeny |
| author_facet | Badanin, Andrey Korotyaev, Evgeny |
| contents | A third-order operator with periodic coefficients is an L-operator in the Lax pair for the Boussinesq equation on a circle. The projection of the divisor of the Floquet solution poles for this operator coincides with the spectrum of the three-point Dirichlet problem. The sign of the norming constant of the three-point problem determines the sheet of the Riemann surface on which the pole lies. We solve the inverse problem for a third-order operator with three-point Dirichlet conditions when the spectrum and norming constant are known. We construct a mapping from the set of coefficients to the set of spectral data and prove that this mapping is an analytic bijection in the neighborhood of zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_06683 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Inverse problem for the divisor of the good Boussinesq equation Badanin, Andrey Korotyaev, Evgeny Mathematical Physics 47E05, 34L20, 34L40 A third-order operator with periodic coefficients is an L-operator in the Lax pair for the Boussinesq equation on a circle. The projection of the divisor of the Floquet solution poles for this operator coincides with the spectrum of the three-point Dirichlet problem. The sign of the norming constant of the three-point problem determines the sheet of the Riemann surface on which the pole lies. We solve the inverse problem for a third-order operator with three-point Dirichlet conditions when the spectrum and norming constant are known. We construct a mapping from the set of coefficients to the set of spectral data and prove that this mapping is an analytic bijection in the neighborhood of zero. |
| title | Inverse problem for the divisor of the good Boussinesq equation |
| topic | Mathematical Physics 47E05, 34L20, 34L40 |
| url | https://arxiv.org/abs/2601.06683 |