We consider existence and stability of dispersion-managed solitons in the two approximations of the periodic nonlinear Schrödinger (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 soliton solutions and their stabilityare 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.
No takes yet. Share an insight, caveat, or question.
Pelinovsky et al. (2003) studied this question.
Synapse has enriched 4 closely related papers on similar clinical questions. Consider them for comparative context: