Averaging of dispersion-managed solitons: Existence and stability

Dmitry E. Pelinovsky, Vadim Zharnitsky

Research output: Contribution to journalArticlepeer-review


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 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.

Original languageEnglish (US)
Pages (from-to)745-776
Number of pages32
JournalSIAM Journal on Applied Mathematics
Issue number3
StatePublished - Jan 2003
Externally publishedYes


  • Averaging theory
  • Dispersion management
  • Errors and convergence of asymptotic series
  • Existence and stability of pulses
  • Gaussian approximation
  • Integral NLS equation
  • Normal form transformations
  • Optical solitons
  • Periodic NLS equation

ASJC Scopus subject areas

  • Applied Mathematics


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