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

David W. McLaughlin; Constance M. Schober

doi:10.1016/0167-2789(92)90013-D

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

David W. McLaughlin, Constance M. Schober

Research output: Contribution to journal › Article

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 language	English (US)
Pages (from-to)	447-465
Number of pages	19
Journal	Physica D: Nonlinear Phenomena
Volume	57
Issue number	3-4
DOIs	https://doi.org/10.1016/0167-2789(92)90013-D
State	Published - Aug 15 1992

Fingerprint

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

Cite this

McLaughlin, D. W., & Schober, C. M. (1992). Chaotic and homoclinic behavior for numerical discretizations of the nonlinear Schrödinger equation. Physica D: Nonlinear Phenomena, 57(3-4), 447-465. https://doi.org/10.1016/0167-2789(92)90013-D

@article{33629ae02a1c430b96a786583f82d65f,

title = "Chaotic and homoclinic behavior for numerical discretizations of the nonlinear Schr{\"o}dinger equation",

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.",

author = "McLaughlin, {David W.} and Schober, {Constance M.}",

year = "1992",

month = aug

day = "15",

doi = "10.1016/0167-2789(92)90013-D",

language = "English (US)",

volume = "57",

pages = "447--465",

journal = "Physica D: Nonlinear Phenomena",

issn = "0167-2789",

publisher = "Elsevier",

number = "3-4",

}

TY - JOUR

T1 - Chaotic and homoclinic behavior for numerical discretizations of the nonlinear Schrödinger equation

AU - McLaughlin, David W.

AU - Schober, Constance M.

PY - 1992/8/15

Y1 - 1992/8/15

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0001127399&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001127399&partnerID=8YFLogxK

U2 - 10.1016/0167-2789(92)90013-D

DO - 10.1016/0167-2789(92)90013-D

M3 - Article

AN - SCOPUS:0001127399

VL - 57

SP - 447

EP - 465

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 3-4

ER -

Access to Document

10.1016/0167-2789(92)90013-D