TRAVELLING WAVES OF FORCED DISCRETE NONLINEAR SCHRODINGER EQUATIONS

被引：9
作者：
Feckan, Michal [1 ,2 ]
Rothos, Vassilis M. [3 ]
机构：
[1] Comenius Univ, Dept Math Anal & Numer Math, Bratislava 84248, Slovakia
[2] Slovak Acad Sci, Inst Math, Bratislava 81473, Slovakia
[3] Aristotle Univ Thessaloniki, Fac Engn, Sch Math Phys & Computat Sci, Thessaloniki 54124, Greece
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2011年 / 4卷 / 05期
关键词：
Forced discrete Schodinger equation; Travelling wave; Bifurcations; HAMILTONIAN-SYSTEMS; SOLITON MOTION; GUIDE ARRAYS; LATTICES; DRIVEN; BREATHERS; STABILITY; EXISTENCE;
D O I：
10.3934/dcdss.2011.4.1129
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We address the existence and bifurcation of periodic travelling wave solutions in forced spatially discrete nonlinear Schrodinger equations with local interactions. We consider polynomial type and bounded nonlinearities. The mathematical methods are based in using Palais-Smale conditions and variational methods. Some generalizations are also discussed.
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收藏
页码：1129 / 1145
页数：17
相关论文
共 31 条
[1]   Discrete Schrodinger equations and dissipative dynamical systems [J].
Abounouh, M. ;
Al Moatassime, H. ;
Chehab, J. P. ;
Dumont, S. ;
Goubet, O. .
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2008, 7 (02) :211-227
[2]  
[Anonymous], 1986, CBMS REG C SER MATH
[3]   Breathers in nonlinear lattices: Existence, linear stability and quantization [J].
Aubry, S .
PHYSICA D-NONLINEAR PHENOMENA, 1997, 103 (1-4) :201-250
[4]   POSSIBLE SOLITON MOTION IN AC-DRIVEN DAMPED NONLINEAR LATTICES [J].
CAI, D ;
SANCHEZ, A ;
BISHOP, AR ;
FALO, F ;
FLORIA, LM .
PHYSICAL REVIEW B, 1994, 50 (13) :9652-9655
[5]   Three-dimensional nonlinear lattices:: From oblique vortices and octupoles to discrete diamonds and vortex cubes -: art. no. 203901 [J].
Carretero-González, R ;
Kevrekidis, PG ;
Malomed, BA ;
Frantzeskakis, DJ .
PHYSICAL REVIEW LETTERS, 2005, 94 (20)
[6]   Multistable solitons in higher-dimensional cubic-quintic nonlinear Schrodinger lattices [J].
Chong, C. ;
Carretero-Gonzalez, R. ;
Malomed, B. A. ;
Kevrekidis, P. G. .
PHYSICA D-NONLINEAR PHENOMENA, 2009, 238 (02) :126-136
[7]   Discretizing light behaviour in linear and nonlinear waveguide lattices [J].
Christodoulides, DN ;
Lederer, F ;
Silberberg, Y .
NATURE, 2003, 424 (6950) :817-823
[8]  
Feckan M., 1997, ANN POL MATH, V67, P43
[9]   Travelling waves in Hamiltonian systems on 2D lattices with nearest neighbour interactions [J].
Feckan, Michal ;
Rothos, Vassilis M. .
NONLINEARITY, 2007, 20 (02) :319-341
[10]   Travelling waves of discrete nonlinear Schrodinger equations with nonlocal interactions [J].
Feckan, Michal ;
Rothos, Vassilis M. .
APPLICABLE ANALYSIS, 2010, 89 (09) :1387-1411
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