Hamiltonian averaging in soliton-bearing systems with a periodically varying dispersion

Optical pulse dynamics in dispersion-managed fiber lines is studied using a combination of a Lagrangian approach and Hamiltonian averaging. By making self-similar transform in the Lagrangian and assuming in the leading order a bell-shaped pulse dynamics, we reduce the original system to a nonautonom ous Hamiltonian system with two variables. Subsequent Hamiltonian averaging gives a function of two variables whose extrema correspond to periodic pul ses. To describe a fine structure of the pulse tails, we further develop Ha miltonian averaging using the complete set of Gauss-Hermite functions and a lso applying averaging in the spectral domain.