Asymptotic behavior of the nonlinear Schrödinger equation with rapidly varying, mean-zero dispersion

Jared C. Bronski, J. Nathan Kutz

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we consider the nonlinear Schrödinger equation with an oscillatory, mean-zero dispersion, which has recently been proposed as an alternative method of dispersion compensation for pulse transmission in optical fibers. Under the assumption that the time scale on which the dispersion changes is short in comparison with the dispersion and nonlinearity time scales, we are able to factor out the leading order contribution of the dispersion which leads to an effective equation for the pulse dynamics. This effective equation is a nonlinear diffusion equation, which is shown by an amplitude-phase decomposition to reduce to the well-known porous medium equation for the amplitude dynamics and a linear, nonconstant coefficient diffusion equation for the phase which is driven by the amplitude.

Original languageEnglish (US)
Pages (from-to)315-329
Number of pages15
JournalPhysica D: Nonlinear Phenomena
Volume108
Issue number3
DOIs
StatePublished - 1997
Externally publishedYes

Keywords

  • Method of stationary phase
  • Nonlinear schrödinger equation
  • Optical fibers
  • Porous medium equation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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