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

Research output: Contribution to journalArticle

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 Schrodinger equation. In general, each choice of the phase factor theta in the projection operator gives a different set of ODEs. For theta = 0 or pi/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. (C) 2004 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)377-382
Number of pages5
JournalOptics Communications
Volume244
DOIs
Publication statusPublished - 2005

Keywords

  • nonlinear Schrodinger equation
  • optical fibers
  • Lagrangian variational method
  • ordinary differential equations
  • projection operator method
  • collective variable
  • RADIATION
  • FIBERS

Cite this

@article{e175e358a7344836bfbc6e1ec1a8368e,
title = "Generalized projection operator method to derive the pulse parameters equations for the nonlinear Schr{\"o}dinger equation",
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 Schrodinger equation. In general, each choice of the phase factor theta in the projection operator gives a different set of ODEs. For theta = 0 or pi/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. (C) 2004 Elsevier B.V. All rights reserved.",
keywords = "nonlinear Schrodinger equation, optical fibers, Lagrangian variational method, ordinary differential equations, projection operator method, collective variable, RADIATION, FIBERS",
author = "Nakkeeran Kaliyaperumal and Wai, {P. K. A.}",
year = "2005",
doi = "10.1016/j.optcom.2004.09.022",
language = "English",
volume = "244",
pages = "377--382",
journal = "Optics Communications",
issn = "0030-4018",
publisher = "Elsevier Science B. V.",

}

TY - JOUR

T1 - Generalized projection operator method to derive the pulse parameters equations for the nonlinear Schrödinger equation

AU - Kaliyaperumal, Nakkeeran

AU - Wai, P. K. A.

PY - 2005

Y1 - 2005

N2 - 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 Schrodinger equation. In general, each choice of the phase factor theta in the projection operator gives a different set of ODEs. For theta = 0 or pi/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. (C) 2004 Elsevier B.V. All rights reserved.

AB - 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 Schrodinger equation. In general, each choice of the phase factor theta in the projection operator gives a different set of ODEs. For theta = 0 or pi/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. (C) 2004 Elsevier B.V. All rights reserved.

KW - nonlinear Schrodinger equation

KW - optical fibers

KW - Lagrangian variational method

KW - ordinary differential equations

KW - projection operator method

KW - collective variable

KW - RADIATION

KW - FIBERS

U2 - 10.1016/j.optcom.2004.09.022

DO - 10.1016/j.optcom.2004.09.022

M3 - Article

VL - 244

SP - 377

EP - 382

JO - Optics Communications

JF - Optics Communications

SN - 0030-4018

ER -