Lax Triples for Integrable Surfaces in Three-Dimensional Space

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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Main Authors: Jan L. Cieśliński, Artur Kobus
Format: Article
Language:English
Published: Hindawi Limited 2016-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2016/8386420
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spelling doaj-d78e6e4dd0954abe84eae2beb986b0302021-07-02T07:22:44ZengHindawi LimitedAdvances 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
collection DOAJ
language English
format Article
sources DOAJ
author Jan L. Cieśliński
Artur Kobus
spellingShingle Jan L. Cieśliński
Artur Kobus
Lax Triples for Integrable Surfaces in Three-Dimensional Space
Advances in Mathematical Physics
author_facet Jan L. Cieśliński
Artur Kobus
author_sort Jan L. Cieśliński
title Lax Triples for Integrable Surfaces in Three-Dimensional Space
title_short 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_sort lax triples for integrable surfaces in three-dimensional space
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2016-01-01
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.
url http://dx.doi.org/10.1155/2016/8386420
work_keys_str_mv AT janlcieslinski laxtriplesforintegrablesurfacesinthreedimensionalspace
AT arturkobus laxtriplesforintegrablesurfacesinthreedimensionalspace
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