On a class of exact solutions of the Ishimori equation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913790347444224 |
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| author | Garifullin, Rustem N. Habibullin, Ismagil T. |
| author_facet | Garifullin, Rustem N. Habibullin, Ismagil T. |
| contents | In this paper, a class of particular solutions of the Ishimori equation is found. This equation is known as the spatially two-dimensional version of the Heisenberg equation, which has important applications in the theory of ferromagnets. It is shown that the two-dimensional Toda-type lattice found earlier by Ferapontov, Shabat and Yamilov is a dressing chain for this equation. Using the integrable reductions of the dressing chain, the authors found an essentially new class of solutions to the Ishimori equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18195 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a class of exact solutions of the Ishimori equation Garifullin, Rustem N. Habibullin, Ismagil T. Exactly Solvable and Integrable Systems Mathematical Physics 35Q51, 35Q56 In this paper, a class of particular solutions of the Ishimori equation is found. This equation is known as the spatially two-dimensional version of the Heisenberg equation, which has important applications in the theory of ferromagnets. It is shown that the two-dimensional Toda-type lattice found earlier by Ferapontov, Shabat and Yamilov is a dressing chain for this equation. Using the integrable reductions of the dressing chain, the authors found an essentially new class of solutions to the Ishimori equation. |
| title | On a class of exact solutions of the Ishimori equation |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics 35Q51, 35Q56 |
| url | https://arxiv.org/abs/2412.18195 |