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Q-deformed solitons and quantum solitons of the Maxwell-Bloch lattice

Andrei Rybin·Jussi Timonen·Gennadii Varzugin·Robin K. Bullough
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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.

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Andrei Rybin, Jussi Timonen, Gennadii Varzugin, Robin K. Bullough. 2000-01-04. Q-deformed solitons and quantum solitons of the Maxwell-Bloch lattice. https://doi.org/10.1088/0305-4470%2F34%2F1%2F312

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