Chaotic and homoclinic behavior for numerical discretizations of the nonlinear Schrödinger equation

David W. McLaughlin, Constance M. Schober

Research output: Contribution to journalArticle

Abstract

Certain conservative discretizations of the NLS can produce irregular behavior. We consider the diagonal discretization as a conservative perturbation of the integrable discretization and study the homoclinic crossings in its nonlinear spectrum. We find that irregularity sets in when two homoclinic structures are present and, in this case, many and continual homoclinic crossings occur throughout the irregular time series. We indicate a Melnikov analysis to study the consequences of this homoclinic behavior.

Original languageEnglish (US)
Pages (from-to)447-465
Number of pages19
JournalPhysica D: Nonlinear Phenomena
Volume57
Issue number3-4
DOIs
StatePublished - Aug 15 1992

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Homoclinic
Nonlinear equations
nonlinear equations
Time series
Nonlinear Equations
Discretization
Irregular
irregularities
Irregularity
perturbation
Perturbation

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistical and Nonlinear Physics

Cite this

Chaotic and homoclinic behavior for numerical discretizations of the nonlinear Schrödinger equation. / McLaughlin, David W.; Schober, Constance M.

In: Physica D: Nonlinear Phenomena, Vol. 57, No. 3-4, 15.08.1992, p. 447-465.

Research output: Contribution to journalArticle

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