Justification of the nonlinear Schrodinger equation in spatially periodic media

被引:42
作者
Busch, Kurt
Schneider, Guido
Tkeshelashvili, Lasha
Uecker, Hannes
机构
[1] Univ Cent Florida, Dept Phys, Orlando, FL 32816 USA
[2] Univ Cent Florida, Coll Opt & Photon, CREOL, Orlando, FL 32816 USA
[3] Univ Cent Florida, Coll Opt & Photon, FPCE, Orlando, FL 32816 USA
[4] Univ Karlsruhe, Inst Math 1, D-76128 Karlsruhe, Germany
来源
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2006年 / 57卷 / 06期
关键词
nonlinear wave equation; periodic media approximation by NLS;
D O I
10.1007/s00033-006-0057-6
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The dynamics of the envelopes of spatially and temporarily oscillating wave packets advancing in spatially periodic media can approximately be described by solutions of a Nonlinear Schrodinger equation. Here we prove estimates for the error made by this formal approximation using Bloch wave analysis, normal form transformations, and Gronwall's inequality.
引用
收藏
页码:905 / 939
页数:35
相关论文
共 35 条
[1]   Optical gap solitons: Past, present, and future; theory and experiments [J].
Aceves, AB .
CHAOS, 2000, 10 (03) :584-589
[2]  
Agrawal, 2001, SOLITONS NONLINEAR W
[3]   Optical pulse propagation in nonlinear photonic crystals [J].
Bhat, NAR ;
Sipe, JE .
PHYSICAL REVIEW E, 2001, 64 (05) :16
[4]  
Bishop A. R., 1980, Physica D, V1D, P1, DOI 10.1016/0167-2789(80)90003-2
[5]   Photonic band structure theory: assessment and perspectives [J].
Busch, K .
COMPTES RENDUS PHYSIQUE, 2002, 3 (01) :53-66
[6]  
CARLES R, 2004, SEMICLASSICAL ASYMPT
[7]  
Colin T, 2002, ASYMPTOTIC ANAL, V31, P69
[8]   Theory of Bose-Einstein condensation in trapped gases [J].
Dalfovo, F ;
Giorgini, S ;
Pitaevskii, LP ;
Stringari, S .
REVIEWS OF MODERN PHYSICS, 1999, 71 (03) :463-512
[9]   Brillouin light scattering studies of confined spin waves: linear and nonlinear confinement [J].
Demokritov, SO ;
Hillebrands, B ;
Slavin, AN .
PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, 2001, 348 (06) :441-489
[10]   ENVELOPE-FUNCTION APPROACH FOR THE ELECTRODYNAMICS OF NONLINEAR PERIODIC STRUCTURES [J].
DESTERKE, CM ;
SIPE, JE .
PHYSICAL REVIEW A, 1988, 38 (10) :5149-5165