Mc'Kean's transformation for 3-rd order operators
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914834230018048 |
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| author | Badanin, Andrey Korotyaev, Evgeny |
| author_facet | Badanin, Andrey Korotyaev, Evgeny |
| contents | We consider a non-self-adjoint third order operator $(y''+py)'+py'+qy$ with 1-periodic coefficients $p,q$. This operator is the L-operator in the Lax pair for the good Boussinesq equation on the circle. In 1981, McKean introduced a transformation that reduces the spectral problem for this operator to a spectral problem for the Hill operator with a potential that depends analytically on the energy. In the present paper we are studying this transformation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09668 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mc'Kean's transformation for 3-rd order operators Badanin, Andrey Korotyaev, Evgeny Mathematical Physics 47E05, 34L20, 34L40 We consider a non-self-adjoint third order operator $(y''+py)'+py'+qy$ with 1-periodic coefficients $p,q$. This operator is the L-operator in the Lax pair for the good Boussinesq equation on the circle. In 1981, McKean introduced a transformation that reduces the spectral problem for this operator to a spectral problem for the Hill operator with a potential that depends analytically on the energy. In the present paper we are studying this transformation. |
| title | Mc'Kean's transformation for 3-rd order operators |
| topic | Mathematical Physics 47E05, 34L20, 34L40 |
| url | https://arxiv.org/abs/2406.09668 |