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 | |
| State | Published - Aug 15 1992 |
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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 journal › Article
}
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.
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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
VL - 57
SP - 447
EP - 465
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
SN - 0167-2789
IS - 3-4
ER -