Dynamics and bifurcations of a planar map modeling dispersion managed breathers

We study a nonautonomous ODE with piecewise-constant coefficients and its a ssociated two-dimensional Poincare mapping. The ODE models variations in am plitude and phase of a pulse propagating in a lossless optical fiber with p eriodically varying dispersion. We derive semiexplicit exact solutions and use them to locate fixed points and to describe their bifurcations and stab ility types. We also discuss the global structure of the Poincare map and i nterpret our results for modulated pulse propagation.