Dynamics and bifurcations of a planar map modeling dispersion managed breathers

We study a nonautonomous ODE with piecewise-constant coefficients and its associated two-dimensional Poincare mapping. The ODE models variations in amplitude and phase of a pulse propagating in a lossless optical fiber with periodically varying dispersion. We derive semiexplicit exact solutions and use them to locate fixed points and to describe their bifurcations and stability types. We also discuss the global structure of the Poincare map and interpret our results for modulated pulse propagation.