WIAS Preprint No. 248, (1996)

Existence and Stability of N-Pulses on Optical Fibers with Phase-Sensitive Amplifiers


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

2010 Mathematics Subject Classification

  • 34C37 35B35 35Q55 78A60


  • homoclinic orbits, bifurcation, stability, optical fibers




The propagation of pulses in optical communication systems in which attenuation is compensated by phase-sensitive amplifiers is investigated. A central issue is whether optical fibers are capable of carrying several pieces of information at the same time. In this paper, multiple pulses are shown to exist for a fourth-order nonlinear diffusion model due to Kutz and co-workers [10]. Moreover, criteria are derived for determining which of these pulses are stable. The pulses arise in a reversible orbit-flip, a homoclinic bifurcation investigated here for the first time. Numerical simulations are used to study multiple pulses far away from the actual bifurcation point. They confirm that properties of the multiple pulses including their stability are surprisingly well predicted by the analysis carried out near the bifurcation.

Appeared in

  • Phys. D, 106 (1997), pp. 167-206

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