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Q-deformed solitons and quantum solitons of the Maxwell-Bloch lattice | | Andrei Rybin
; Jussi Timonen
; Gennadii Varzugin
; Robin K. Bullough
; | | Date: |
4 Dec 1999 | | Journal: | J. Phys. A: Math. Gen., 34, 157 (2001) | | Subject: | Exactly Solvable and Integrable Systems | nlin.SI | | Abstract: | We report for the first time exact solutions of a completely integrable nonlinear lattice system for which the dynamical variables satisfy a q-deformed Lie algebra - the Lie-Poisson algebra su_q(2). The system considered is a q-deformed lattice for which in continuum limit the equations of motion become the envelope Maxwell-Bloch (or SIT) equations describing the resonant interaction of light with a nonlinear dielectric. Thus the N-soliton solutions we here report are the natural q-deformations, necessary for a lattice, of the well-known multi-soliton and breather solutions of self-induced transparency (SIT). The method we use to find these solutions is a generalization of the Darboux-Backlund dressing method. The extension of these results to quantum solitons is sketched. | | Source: | arXiv, nlin.SI/0001006 | | Services: | Forum | Review | PDF | Favorites | |
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