WIAS Preprint No. 189, (1995)

Stability of pulses on optical fibers with phase-sensitive amplifiers



Authors

  • Alexander, James C.
  • Grillakis, Manoussos G.
  • Jones, Christopher K.R.T.
  • Sandstede, Björn

2010 Mathematics Subject Classification

  • 35Q55 35B35 78A60

Keywords

  • solitons, nonlinear optical pulse propagation, optical fibers, stability

Abstract

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.

Appeared in

  • Z. Angew. Math. Phys., 48 (1997), pp. 175-192

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