6533b820fe1ef96bd127a5ff
RESEARCH PRODUCT
q-deformed solitons and quantum solitons of the Maxwell-Bloch lattice
R. K. BulloughJussi TimonenAndrei RybinG. G. Varzuginsubject
PhysicsNonlinear Sciences - Exactly Solvable and Integrable SystemsIntegrable systemBreatherFOS: Physical sciencesGeneral Physics and AstronomyEquations of motionStatistical and Nonlinear PhysicsDielectricNonlinear systemNonlinear Sciences::Exactly Solvable and Integrable SystemsLattice (order)Lie algebraExactly Solvable and Integrable Systems (nlin.SI)QuantumMathematical PhysicsMathematical physicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2000-01-04 | Journal of Physics A: Mathematical and General |