TY - JOUR
T1 - Chaotic and homoclinic behavior for numerical discretizations of the nonlinear Schrödinger equation
AU - McLaughlin, David W.
AU - Schober, Constance M.
N1 - Funding Information:
correspondences, and A. Calini and N. Ereolani for many useful discussions. The work reported here was supported by the NSF under grant #DMS8703397 and the United States Air Force under grant #AFOSRF49620-86-C0130.
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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U2 - 10.1016/0167-2789(92)90013-D
DO - 10.1016/0167-2789(92)90013-D
M3 - Article
AN - SCOPUS:0001127399
SN - 0167-2789
VL - 57
SP - 447
EP - 465
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
IS - 3-4
ER -