On symmetries of the Gibbons-Tsarev equation
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2018
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| _version_ | 1866929282335375360 |
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| author | Baran, H. Blaschke, P. Krasil'shchik, I. S. Marvan, M. |
| author_facet | Baran, H. Blaschke, P. Krasil'shchik, I. S. Marvan, M. |
| contents | We study the Gibbons-Tsarev equation $z_{yy} + z_x z_{xy} - z_y z_{xx} + 1 = 0$ and, using the known Lax pair, we construct infinite series of conservation laws and the algebra of nonlocal symmetries in the covering associated with these conservation laws. We prove that the algebra is isomorphic to the Witt algebra. Finally, we show that the constructed symmetries are unique in the class of polynomial ones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1811_08199 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | On symmetries of the Gibbons-Tsarev equation Baran, H. Blaschke, P. Krasil'shchik, I. S. Marvan, M. Exactly Solvable and Integrable Systems 35B06 We study the Gibbons-Tsarev equation $z_{yy} + z_x z_{xy} - z_y z_{xx} + 1 = 0$ and, using the known Lax pair, we construct infinite series of conservation laws and the algebra of nonlocal symmetries in the covering associated with these conservation laws. We prove that the algebra is isomorphic to the Witt algebra. Finally, we show that the constructed symmetries are unique in the class of polynomial ones. |
| title | On symmetries of the Gibbons-Tsarev equation |
| topic | Exactly Solvable and Integrable Systems 35B06 |
| url | https://arxiv.org/abs/1811.08199 |