@article{13e013dfa74c4d94984d55b338be4419,
title = "Discretization effects in the nonlinear Schr{\"o}dinger equation",
abstract = "We show that discretization effects in finite-difference simulations of blowup solutions of the nonlinear Schr{\"o}dinger equation (NLS) initially accelerate self focusing but later arrest the collapse, resulting instead in focusing-defocusing oscillations. The modified equation of the semi-discrete NLS, which is the NLS with high-order anisotropic dispersion, captures the arrest of collapse but not the subsequent oscillations. Discretization effects in perturbed NLS equations are also discussed.",
keywords = "Beam collapse, Blowup, Modified equation, Self focusing, Singularity formation",
author = "Gadi Fibich and Boaz Ilan",
note = "Funding Information: The authors would like to thank Mu Mo for pointing out the applicability of their previous work [9] to discretization effects. This research was supported by Grant No. 97-00127 and Grant No. 2000311 from the United States–Israel Binational Science Foundation (BSF), Jerusalem, Israel.",
year = "2003",
month = jan,
doi = "10.1016/S0168-9274(02)00112-5",
language = "אנגלית",
volume = "44",
pages = "63--75",
journal = "Applied Numerical Mathematics",
issn = "0168-9274",
publisher = "Elsevier B.V.",
number = "1-2",
}