A veraging of dispersion-managed pulses: existence and stability
01 January 2003
We consider existence and stability of dispersion-managed pulses in the two approximations of the periodic NLS equation: (i) a dynamical system for a Gaussian pulse and (ii) an average integral NLS equation. We apply normal form transformations for finite-dimensional and infinite-dimensional Hamiltonian systems with periodic coefficients. First-order corrections to the leading-order averaged Hamiltonian are derived explicitly for both approximations. Bifurcations of pulse solutions and their stability are studied by analysis of critical points of the first-order averaged Hamiltonians. The validity of the averaging procedure is verfied and the presence of ground states corresponding to dispersionn-managed pulses in the averaged Hamiltonian is established.