Generalized projection operator method to derive the pulse parameters equations for the nonlinear Schrödinger equation

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29 Citations (Scopus)

Abstract

We present a novel projection operator method for deriving the ordinary differential equations (ODEs) which describe the pulse parameters dynamics of an ansatz function for the nonlinear Schrödinger equation. In general, each choice of the phase factor θ in the projection operator gives a different set of ODEs. For θ = 0 or π/2, we prove that the corresponding projection operator scheme is equivalent to the Lagrangian method or the bare approximation of the collective variable theory. Which set of ODEs best approximates the pulse parameter dynamics depends on the ansatz used.
Original languageEnglish
Pages (from-to)377-382
Number of pages6
JournalOptics Communications
Volume244
Issue number1-6
DOIs
Publication statusPublished - 3 Jan 2005

Keywords

  • Collective variable
  • Lagrangian variational method
  • Nonlinear Schrödinger equation
  • Optical fibers
  • Ordinary differential equations
  • Projection operator method

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Atomic and Molecular Physics, and Optics
  • Physical and Theoretical Chemistry
  • Electrical and Electronic Engineering

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