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This article is cited in 5 scientific papers (total in 5 papers)
On the Integrability of Supersymmetric Versions of the Structural Equations for Conformally Parametrized Surfaces
Sébastien Bertranda, Alfred M. Grundlandbc, Alexander J. Haritonc a Department of Mathematics and Statistics, Université de Montréal, Montréal CP 6128 (QC) H3C 3J7, Canada
b Department of Mathematics and Computer Science, Université du Québec, Trois-Rivières, CP 500 (QC) G9A 5H7, Canada
c Centre de Recherches Mathématiques, Université de Montréal, Montréal CP 6128 (QC) H3C 3J7, Canada
Abstract:
The paper presents the bosonic and fermionic supersymmetric extensions of the structural equations describing conformally parametrized surfaces immersed in a Grasmann superspace, based on the authors' earlier results. A detailed analysis of the symmetry properties of both the classical and supersymmetric versions of the Gauss–Weingarten equations is performed. A supersymmetric generalization of the conjecture establishing the necessary conditions for a system to be integrable in the sense of soliton theory is formulated and illustrated by the examples of supersymmetric versions of the sine-Gordon equation and the Gauss–Codazzi equations.
Keywords:
supersymmetric models; Lie superalgebras; symmetry reduction; conformally parametrized surfaces; integrability.
Received: February 11, 2015; in final form June 9, 2015; Published online June 17, 2015
Citation:
Sébastien Bertrand, Alfred M. Grundland, Alexander J. Hariton, “On the Integrability of Supersymmetric Versions of the Structural Equations for Conformally Parametrized Surfaces”, SIGMA, 11 (2015), 046, 16 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1027 https://www.mathnet.ru/eng/sigma/v11/p46
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