Interaction of modulated pulses in the nonlinear Schrodinger equation with periodic potential

被引：18

作者：

Giannoulis, Johannes ^{[3
]}

Mielke, Alexander ^{[4
,5
]}

Sparber, Christof ^{[1
,2
]}

机构：

[1] Univ Vienna, Wolfgang Pauli Inst Vienna, A-1090 Vienna, Austria

[2] Univ Vienna, Fac Math, A-1090 Vienna, Austria

[3] Tech Univ Munich, Zentrum Math, D-85747 Garching, Germany

[4] Weierstrass Inst Angew Anal & Stochast, D-10117 Berlin, Germany

[5] Humboldt Univ, Inst Math, D-12489 Berlin, Germany

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2008年 / 245卷 / 04期

关键词：

nonlinear Schrodinger equation; Bloch eigenvalue problem; two scale asymptotics; modulation equations; four-wave interaction;

D O I：

10.1016/j.jde.2008.05.001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a cubic nonlinear Schrodinger equation with periodic potential. In a semiclassical scaling the nonlinear interaction of modulated pulses concentrated in one or several Bloch bands is studied. The notion of closed mode systems is introduced which allows for the rigorous derivation of a finite system of amplitude equations describing the macroscopic interaction of these pulses. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：939 / 963

页数：25

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