Stability of Pulses in Nonlinear Optical Fibers Using Phase-Sensitive Amplifiers

This paper considers the stability of soliton-like pulses propagating in nonlinear optical bers with periodically-spaced phase-sensitive ampli ers, a situation where the averaged pulse evolution is governed by a fourth-order nonlinear di usion equation similar to the KuramotoSivashinsky or Swift-Hohenberg equations. A bifurcation and stability analysis of this averaged equation is carried out, and in the limit of small ampli er spacing, a steady-state pulse solution is shown to be asympotically stable. Furthermore, both a saddle-node bifurcation and a subcritical bifurcation from the zero solution are found. Analytical results are con rmed using the bifurcation software package auto. The analysis provides evidence for the existence of stable pulse solutions for a wide range of parameter values, including those corresponding to physically realizable soliton communications systems.