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Symmetries of the SelfSimilar Potentials  V.Spiridonov
;  Date: 
1 Mar 1993  Subject:  hepth  Abstract:  An application of the particular type of nonlinear operator algebras to spectral problems is outlined. These algebras are associated with a set of onedimensional selfsimilar potentials, arising due to the qperiodic closure f_{j+N}(x)=qf_j(qx), k_{j+N}=q^2 k_j of a chain of coupled Riccati equations (dressing chain). Such closure describes qdeformation of the finitegap and related potentials. The N=1 case corresponds to the qoscillator spectrum generating algebra. At N=2 one gets a qconformal quantum mechanics, and N=3 set of equations describes a deformation of the Painleve IV transcendent.  Source:  arXiv, hepth/9303004  Services:  Forum  Review  PDF  Favorites 


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