Averaging of Dispersion-Managed Solitons: Existence and Stability

We consider existence and stability of dispersion-managed solitons in the two ap- proximations of the periodic nonlinear Schrodinger (NLS) equation: (i) a dynamicalsystem for a Gaussian pulse and (ii) an average integral NLS equation. We apply normal form transformations for finite-dimensionaland infinite-dimensionalHamil tonian systems with periodic coefficients. First- order corrections to the leading-order averaged Hamiltonian are derived explicitly for both approxi- mations. Bifurcations of soliton solutions and their stability are studied by analysis of critical points of the first-order averaged Hamiltonians. The validity of the averaging procedure is verified and the presence of ground states corresponding to dispersion-managed solitons in the averaged Hamiltonian is established.

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