Voss surfaces in sine-Gordon hierarchies
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909913661308928 |
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| author | Marvan, Michal |
| author_facet | Marvan, Michal |
| contents | We explore a method, initiated by Guichard in 1890, which allows to generate sequences of Voss surfaces by quadratures, starting from an arbitrarily chosen pseudospherical surface and a seed solution of the Moutard equation, by means of two simple transformations. In this paper we 1) identify the Guichard transformations with the well-known recursion operators for symmetries of the sine-Gordon equation; 2) prove a lemma which allows us to derive the length of Guichard's sequences from the invariance properties of the initial sine-Gordon solution; 3) introduce an extended class of inverted operators, increasing the number of Voss surfaces obtainable by quadratures. Several Voss nets are presented explicitly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_15558 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Voss surfaces in sine-Gordon hierarchies Marvan, Michal Differential Geometry Exactly Solvable and Integrable Systems 35A30, 37K10, 53A05, 58J70 We explore a method, initiated by Guichard in 1890, which allows to generate sequences of Voss surfaces by quadratures, starting from an arbitrarily chosen pseudospherical surface and a seed solution of the Moutard equation, by means of two simple transformations. In this paper we 1) identify the Guichard transformations with the well-known recursion operators for symmetries of the sine-Gordon equation; 2) prove a lemma which allows us to derive the length of Guichard's sequences from the invariance properties of the initial sine-Gordon solution; 3) introduce an extended class of inverted operators, increasing the number of Voss surfaces obtainable by quadratures. Several Voss nets are presented explicitly. |
| title | Voss surfaces in sine-Gordon hierarchies |
| topic | Differential Geometry Exactly Solvable and Integrable Systems 35A30, 37K10, 53A05, 58J70 |
| url | https://arxiv.org/abs/2511.15558 |