Stable pulse solutions for the nonlinear Schrödinger equation with higher order dispersion management

Jamison T. Moesert, Christopher K.R.T. Jones, Vadim Zharnitsky

Research output: Contribution to journalArticlepeer-review

Abstract

The evolution of optical pulses in fiber optic communication systems with strong, higher order dispersion management is modeled by a cubic nonlinear Schrödinger equation with periodically varying linear dispersion at second and third order. Through an averaging procedure, we derive an approximate model for the slow evolution of such pulses and show that this system possesses a stable ground state solution. Furthermore, we characterize the ground state numerically. The results explain the experimental observation of higher order dispersion managed solitons, providing theoretical justification for modern communication systems design.

Original languageEnglish (US)
Pages (from-to)1486-1511
Number of pages26
JournalSIAM Journal on Mathematical Analysis
Volume35
Issue number6
DOIs
StatePublished - 2004

Keywords

  • Higher order dispersion management
  • Homogenization
  • Nonlinear schrödinger equation
  • Periodic media
  • Solitary waves
  • Stability

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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