TY - JOUR
T1 - Discretization effects in the nonlinear Schrödinger equation
AU - Fibich, Gadi
AU - Ilan, Boaz
N1 - 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.
PY - 2003/1
Y1 - 2003/1
N2 - We show that discretization effects in finite-difference simulations of blowup solutions of the nonlinear Schrödinger 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.
AB - We show that discretization effects in finite-difference simulations of blowup solutions of the nonlinear Schrödinger 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.
KW - Beam collapse
KW - Blowup
KW - Modified equation
KW - Self focusing
KW - Singularity formation
UR - http://www.scopus.com/inward/record.url?scp=0037214146&partnerID=8YFLogxK
U2 - 10.1016/S0168-9274(02)00112-5
DO - 10.1016/S0168-9274(02)00112-5
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AN - SCOPUS:0037214146
VL - 44
SP - 63
EP - 75
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
SN - 0168-9274
IS - 1-2
ER -