Discretization effects in the nonlinear Schrodinger equation

被引：16

作者：

Fibich, G ^{[1
]}

Ilan, B ^{[1
]}

机构：

[1] Tel Aviv Univ, Dept Appl Math, IL-69978 Tel Aviv, Israel

来源：

APPLIED NUMERICAL MATHEMATICS | 2003年 / 44卷 / 1-2期

关键词：

blowup; singularity formation; beam collapse; self focusing; modified equation;

D O I：

10.1016/S0168-9274(02)00112-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that discretization effects in finite-difference simulations of blowup solutions of the nonlinear Schrodinger 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. (C) 2002 IMACS. Published by Elsevier Science B.V. All rights reserved.

引用

页码：63 / 75

页数：13

共 22 条

[1] ENERGY LOCALIZATION IN NONLINEAR FIBER ARRAYS - COLLAPSE-EFFECT COMPRESSOR [J].

ACEVES, AB ;

LUTHER, GG ;

DEANGELIS, C ;

RUBENCHIK, AM ;

TURITSYN, SK .

PHYSICAL REVIEW LETTERS, 1995, 75 (01) :73-76

[2]

AKRIVIS G, 1993, ADV COMPUTER MATH IT, P85

[3] SUBCRITICAL LOCALIZATION IN THE DISCRETE NONLINEAR SCHRODINGER-EQUATION WITH ARBITRARY POWER NONLINEARITY [J].

BANG, O ;

RASMUSSEN, JJ ;

CHRISTIANSEN, PL .

NONLINEARITY, 1994, 7 (01) :205-218

[4] Amalgamation of interacting light beamlets in Kerr-type media [J].

Berge, L ;

Schmidt, MR ;

Rasmussen, JJ ;

Christiansen, PL ;

Rasmussen, KO .

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B-OPTICAL PHYSICS, 1997, 14 (10) :2550-2562

[5] VECTOR THEORY OF SELF-FOCUSING OF AN OPTICAL BEAM IN KERR MEDIA [J].

CHI, S ;

GUO, Q .

OPTICS LETTERS, 1995, 20 (15) :1598-1600

[6] Self-focusing with fourth-order dispersion [J].

Fibich, G ;

Ilan, B ;

Papanicolaou, G .

SIAM JOURNAL ON APPLIED MATHEMATICS, 2002, 62 (04) :1437-1462

[7] Deterministic vectorial effects lead to multiple filamentation [J].

Fibich, G ;

Ilan, B .

OPTICS LETTERS, 2001, 26 (11) :840-842

[8] Vectorial and random effects in self-focusing and in multiple filamentation [J].

Fibich, G ;

Ilan, B .

PHYSICA D, 2001, 157 (1-2) :112-146

[9] A modulation method for self-focusing in the perturbed critical nonlinear Schrodinger equation [J].

Fibich, G ;

Papanicolaou, G .

PHYSICS LETTERS A, 1998, 239 (03) :167-173

[10] Self-focusing in the perturbed and unperturbed nonlinear Schrodinger equation in critical dimension [J].

Fibich, G ;

Papanicolaou, G .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1999, 60 (01) :183-240

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