Abstract
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 language | English (US) |
|---|---|
| Pages (from-to) | 745-776 |
| Number of pages | 32 |
| Journal | SIAM Journal on Applied Mathematics |
| Volume | 63 |
| Issue number | 3 |
| DOIs | |
| State | Published - Jan 2003 |
| Externally published | Yes |
Keywords
- 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