Lax Triples for Integrable Surfaces in Three-Dimensional Space
We study Lax triples (i.e., Lax representations consisting of three linear equations) associated with families of surfaces immersed in three-dimensional Euclidean space E3. We begin with a natural integrable deformation of the principal chiral model. Then, we show that all deformations linear in the...
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| Format: | Article |
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Wiley
2016-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2016/8386420 |
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| author | Jan L. Cieśliński Artur Kobus |
| author_facet | Jan L. Cieśliński Artur Kobus |
| author_sort | Jan L. Cieśliński |
| collection | DOAJ |
| description | We study Lax triples (i.e., Lax representations consisting of three linear equations) associated with families of surfaces immersed in three-dimensional Euclidean space E3. We begin with a natural integrable deformation of the principal chiral model. Then, we show that all deformations linear in the spectral parameter λ are trivial unless we admit Lax representations in a larger space. We present an explicit example of triply orthogonal systems with Lax representation in the group Spin(6). Finally, the obtained results are interpreted in the context of the soliton surfaces approach. |
| format | Article |
| id | doaj-art-d78e6e4dd0954abe84eae2beb986b030 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-d78e6e4dd0954abe84eae2beb986b0302025-02-03T05:52:22ZengWileyAdvances in Mathematical Physics1687-91201687-91392016-01-01201610.1155/2016/83864208386420Lax Triples for Integrable Surfaces in Three-Dimensional SpaceJan L. Cieśliński0Artur Kobus1Uniwersytet w Białymstoku, Wydział Fizyki, Ulica Ciołkowskiego 1L, 15-245 Białystok, PolandPolitechnika Białostocka, Wydział Budownictwa i Inżynierii Środowiska, Ulica Wiejska 45E, 15-351 Białystok, PolandWe study Lax triples (i.e., Lax representations consisting of three linear equations) associated with families of surfaces immersed in three-dimensional Euclidean space E3. We begin with a natural integrable deformation of the principal chiral model. Then, we show that all deformations linear in the spectral parameter λ are trivial unless we admit Lax representations in a larger space. We present an explicit example of triply orthogonal systems with Lax representation in the group Spin(6). Finally, the obtained results are interpreted in the context of the soliton surfaces approach.http://dx.doi.org/10.1155/2016/8386420 |
| spellingShingle | Jan L. Cieśliński Artur Kobus Lax Triples for Integrable Surfaces in Three-Dimensional Space Advances in Mathematical Physics |
| title | Lax Triples for Integrable Surfaces in Three-Dimensional Space |
| title_full | Lax Triples for Integrable Surfaces in Three-Dimensional Space |
| title_fullStr | Lax Triples for Integrable Surfaces in Three-Dimensional Space |
| title_full_unstemmed | Lax Triples for Integrable Surfaces in Three-Dimensional Space |
| title_short | Lax Triples for Integrable Surfaces in Three-Dimensional Space |
| title_sort | lax triples for integrable surfaces in three dimensional space |
| url | http://dx.doi.org/10.1155/2016/8386420 |
| work_keys_str_mv | AT janlcieslinski laxtriplesforintegrablesurfacesinthreedimensionalspace AT arturkobus laxtriplesforintegrablesurfacesinthreedimensionalspace |