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Deformation surfaces, integrable systems and Chern - Simons theory | | L. Martina
; Kur. Myrzakul
; R. Myrzakulov
; G. Soliani
; | | Date: |
23 Jun 2000 | | Journal: | J.Math.Phys. 42 (2001) 1397-1417 | | Subject: | Exactly Solvable and Integrable Systems; Pattern Formation and Solitons | nlin.SI nlin.PS | | Abstract: | A few years ago, some of us devised a method to obtain integrable systems in (2+1)-dimensions from the classical non-Abelian pure Chern-Simons action via reduction of the gauge connection in Hermitian symmetric spaces. In this paper we show that the methods developed in studying classical non-Abelian pure Chern-Simons actions, can be naturally implemented by means of a geometrical interpretation of such systems. The Chern-Simons equation of motion turns out to be related to time evolving 2-dimensional surfaces in such a way that these deformations are both locally compatible with the Gauss-Mainardi-Codazzi equations and completely integrable. The properties of these relationships are investigated together with the most relevant consequences. Explicit examples of integrable surface deformations are displayed and discussed. | | Source: | arXiv, nlin.SI/0006039 | | Services: | Forum | Review | PDF | Favorites | |
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