Stability of pulses in nonlinear optical fibers using phase-sensitive amplifiers

We consider the stability of soliton-like pulses propagating in nonlinear optical fibers with periodically spaced phase-sensitive amplifiers, a situation where the averaged pulse evolution is governed by a fourth-order nonlinear diffusion equation similar to the Kuramoto-Sivashinsky or Swift-Hohenberg equations. A bifurcation and stability analysis of this averaged equation is carried out, and in the limit of small amplifier spacing, a steady-state pulse solution is shown to be asymptotically stable. Furthermore, both a saddle-node bifurcation and a subcritical bifurcation from the zero solution are found. Analytical results are confirmed 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.