Integrable discretization of nonlinear Schrodinger equation and its application with Fourier pseudo-spectral method

被引：3

作者：

Zhang, Y. ^{[1
]}

Hu, X. B. ^{[1
]}

Tam, H. W. ^{[2
]}

机构：

[1] Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing, Peoples R China

[2] Hong Kong Baptist Univ, Dept Comp Sci, Hongkong, Peoples R China

来源：

NUMERICAL ALGORITHMS | 2015年 / 69卷 / 04期

基金：

中国国家自然科学基金;

关键词：

NLS equation; Integrable discretization; Infinite conservation quantities; Fourier pseudo-spectral method; DISCRETE SOLITON-EQUATIONS; PARTIAL DIFFERENCE-EQUATIONS; DISPERSIVE DIELECTRIC FIBERS; NUMERICALLY INDUCED CHAOS; EVOLUTION-EQUATIONS; BACKLUND-TRANSFORMATIONS; OPTICAL PULSES; TIME; TRANSMISSION; SCHEMES;

D O I：

10.1007/s11075-014-9928-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A new integrable discretization of the nonlinear SchrAodinger (NLS) equation is presented. Different from the one given by Ablowitz and Ladik, we discretize the time variable in this paper. The new discrete system converges to the NLS equation when we take a standard limit and has the same scattering operator as the original NLS equation. This indicates that both the new system and the NLS equation possess the same set of infinite conservation quantities. By applying the Fourier pseudo-spectral method to the space variable, we calculate the first five conservation quantities at different times. The numerical results indeed verify the conservation properties.

引用

页码：839 / 862

页数：24

共 55 条

[21] HIROTA EQUATION AS AN EXAMPLE OF AN INTEGRABLE SYMPLECTIC MAP
FADDEEV, L
VOLKOV, AY
[J]. LETTERS IN MATHEMATICAL PHYSICS, 1994, 32 (02) : 125 - 135
[22] Fornberg B., 1998, A Practical Guide to Pseudospectral Methods
[23] Dark solitons in atomic Bose-Einstein condensates: from theory to experiments
Frantzeskakis, D. J.
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2010, 43 (21)
[24] TRANSMISSION OF STATIONARY NONLINEAR OPTICAL PULSES IN DISPERSIVE DIELECTRIC FIBERS .1. ANOMALOUS DISPERSION
HASEGAWA, A
TAPPERT, F
[J]. APPLIED PHYSICS LETTERS, 1973, 23 (03) : 142 - 144
[25] TRANSMISSION OF STATIONARY NONLINEAR OPTICAL PULSES IN DISPERSIVE DIELECTRIC FIBERS .2. NORMAL DISPERSION
HASEGAWA, A
TAPPERT, F
[J]. APPLIED PHYSICS LETTERS, 1973, 23 (04) : 171 - 172
[26] NUMERICALLY INDUCED CHAOS IN THE NONLINEAR SCHRODINGER-EQUATION
HERBST, BM
ABLOWITZ, MJ
[J]. PHYSICAL REVIEW LETTERS, 1989, 62 (18) : 2065 - 2068
[27] NON-LINEAR PARTIAL DIFFERENCE EQUATIONS .2. DISCRETE-TIME TODA EQUATION
HIROTA, R
[J]. JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 1977, 43 (06) : 2074 - 2078
[28] NONLINEAR PARTIAL DIFFERENCE EQUATIONS .1. DIFFERENCE ANALOG OF KORTEWEG-DEVRIES EQUATION
HIROTA, R
[J]. JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 1977, 43 (04) : 1424 - 1433
[29] NON-LINEAR PARTIAL DIFFERENCE EQUATIONS 3 - DISCRETE SINE-GORDON EQUATION
HIROTA, R
[J]. JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 1977, 43 (06) : 2079 - 2086
[30] Hirota R., 2004, The Direct Method in Soliton Theory, DOI 10.1017/CBO9780511543043

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