Stability of pulses on optical fibers with phase-sensitive amplifiers
- Alexander, James C.
- Grillakis, Manoussos G.
- Jones, Christopher K.R.T.
- Sandstede, Björn
2010 Mathematics Subject Classification
- 35Q55 35B35 78A60
- solitons, nonlinear optical pulse propagation, optical fibers, stability
Pulse stability is crucial to the effective propagation of information in a soliton-based optical communication system. It is shown in this paper that pulses in optical fibers, for which attenuation is compensated by phase-sensitive amplifiers, are stable over a large range of parameter values. A fourth-order nonlinear diffusion model due to Kath and co-workers is used. The stability proof invokes a number of mathematical techniques, including the Evans function and Grillakis' functional analytic approach.
- Z. Angew. Math. Phys., 48 (1997), pp. 175-192