Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2000-01-04
J. Phys. A: Math. Gen., 34, 157 (2001)
Nonlinear Sciences
Exactly Solvable and Integrable Systems
12 pages
Scientific paper
10.1088/0305-4470/34/1/312
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.
Bullough Robin K.
Rybin Andrei
Timonen Jussi
Varzugin Gennadii
No associations
LandOfFree
Q-deformed solitons and quantum solitons of the Maxwell-Bloch lattice does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Q-deformed solitons and quantum solitons of the Maxwell-Bloch lattice, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Q-deformed solitons and quantum solitons of the Maxwell-Bloch lattice will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-110469