Nonlinear Schrodinger Equations and Their Spectral Semi-Discretizations Over Long Times

被引：36

作者：

Gauckler, Ludwig ^{[1
]}

Lubich, Christian ^{[1
]}

机构：

[1] Univ Tubingen, Math Inst, D-72076 Tubingen, Germany

来源：

FOUNDATIONS OF COMPUTATIONAL MATHEMATICS | 2010年 / 10卷 / 02期

关键词：

Nonlinear Schrodinger equation; Spectral semi-discretization; Long-time behavior; Near-conservation of actions; energy; and momentum; Modulated Fourier expansion; WAVE-EQUATIONS; DIFFERENTIAL-EQUATIONS; CONSERVATION; ENERGY;

D O I：

10.1007/s10208-010-9059-z

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Cubic Schrodinger equations with small initial data (or small nonlinearity) and their spectral semi-discretizations in space are analyzed. It is shown that along both the solution of the nonlinear Schrodinger equation as well as the solution of the semi-discretized equation the actions of the linear Schrodinger equation are approximately conserved over long times. This also allows us to show approximate conservation of energy and momentum along the solution of the semi-discretized equation over long times. These results are obtained by analyzing a modulated Fourier expansion in time. They are valid in arbitrary spatial dimension.

引用

页码：141 / 169

页数：29

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