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Deformation of surfaces, integrable systems and Self-Dual Yang-Mills equation | | T.A.Kozhamkulov
; Kuralay Myrzakul
; R.Myrzakulov
; | | Date: |
25 Jul 2002 | | Subject: | Exactly Solvable and Integrable Systems | nlin.SI | | Abstract: | We conjecture that many (maybe all) integrable equations and spin systems in 2+1 dimensions can be obtained from the (2+1)-dimensional Gauss-Mainardi-Codazzi and Gauss-Weingarten equations, respectively. We also show that the (2+1)-dimensional Gauss-Mainardi-Codazzi equation which describes the deformation (motion) of surfaces is the exact reduction of the Yang-Mills-Higgs-Bogomolny and Self-Dual Yang-Mills equations. On the basis of this observation, we suggest that the (2+1)-dimensional Gauss-Mainardi-Codazzi equation is a candidate to be integrable and the associated linear problem (Lax representation) with the spectral parameter is presented. | | Source: | arXiv, nlin.SI/0207046 | | Services: | Forum | Review | PDF | Favorites | |
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