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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2211.12895 |
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| _version_ | 1866909111145201664 |
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| author | Smirnov, Aleksandr O. Caplieva, Aleksandra A. |
| author_facet | Smirnov, Aleksandr O. Caplieva, Aleksandra A. |
| contents | In our work a hierarchy of integrable vector nonlinear differential equations depending on the functional parameter $r$ is constructed using a monodromy matrix. The first equation of this hierarchy for $r=α(\mathbf{p}^t\mathbf{q})$ is vector analogue of the Kundu-Eckhaus equation. When $α=0$, the equations of this hierarchy turn into equations of the Manakov system hierarchy. New elliptic solutions to vector analogue of the Kundu-Eckhaus and Manakov system are presented. In conclusion, it is shown that there exist linear transformations of solutions to vector integrable nonlinear equations into other solutions to the same equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_12895 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The vector form of Kundu-Eckhaus equation and its simplest solutions Smirnov, Aleksandr O. Caplieva, Aleksandra A. Exactly Solvable and Integrable Systems Mathematical Physics In our work a hierarchy of integrable vector nonlinear differential equations depending on the functional parameter $r$ is constructed using a monodromy matrix. The first equation of this hierarchy for $r=α(\mathbf{p}^t\mathbf{q})$ is vector analogue of the Kundu-Eckhaus equation. When $α=0$, the equations of this hierarchy turn into equations of the Manakov system hierarchy. New elliptic solutions to vector analogue of the Kundu-Eckhaus and Manakov system are presented. In conclusion, it is shown that there exist linear transformations of solutions to vector integrable nonlinear equations into other solutions to the same equations. |
| title | The vector form of Kundu-Eckhaus equation and its simplest solutions |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics |
| url | https://arxiv.org/abs/2211.12895 |