SOLITON-LIKE STATES IN A ONE-DIMENSIONAL NONLINEAR SCHRODINGER-EQUATION WITH A DETERMINISTIC APERIODIC POTENTIAL

被引:21
作者
JOHANSSON, M
RIKLUND, R
机构
[1] Department of Physics and Measurement Technology, University of Linköping
来源
PHYSICAL REVIEW B | 1994年 / 49卷 / 10期
关键词
D O I
10.1103/PhysRevB.49.6587
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
We study the electronic properties of a one-dimensional deterministic aperiodic nonlinear lattice using a tight-binding form of the nonlinear Schrodinger equation. A nonlinear eigenvalue problem is solved for self-consistent solutions, and the corresponding transmission problem is studied using a two-dimensional nonlinear mapping. When the aperiodicity is chosen according to the True-Morse sequence and the nonlinearity is small, we find solitonlike solutions in a similar way as for a periodic lattice. The coupling of an incoming plane wave to these structures results in peaks of perfect transmission in the transmission gaps of the corresponding linear model. Transmission peaks due to dark solitons, and to combinations of several weakly interacting solitons, so called ''multisolitons'' or ''soliton trains'' are also found. For larger nonlinearity we find that bounded and diverging solutions are mixed in an intricate pattern; the set of energy values yielding bounded orbits for a given nolinearity strength showing a Cantor-like structure reminiscent of the linear Thue-Morse system.
引用
收藏
页码:6587 / 6600
页数:14
相关论文
共 57 条
[21]   SOLITON-LIKE STRUCTURES AND THEIR SELF-SIMILARITY IN NONLINEAR FIBONACCI MULTILAYERED MEDIA [J].
GUPTA, SD ;
RAY, DS .
PHYSICAL REVIEW B, 1989, 40 (15) :10604-10606
[22]   LOCALIZATION PROBLEM IN OPTICS - NONLINEAR QUASI-PERIODIC MEDIA [J].
GUPTA, SD ;
RAY, DS .
PHYSICAL REVIEW B, 1990, 41 (12) :8047-8053
[23]   THE EFFECT OF AN INTERELECTRON INTERACTION ON ELECTRONIC-PROPERTIES IN ONE-DIMENSIONAL QUASI-PERIODIC SYSTEMS [J].
HIRAMOTO, H .
JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 1990, 59 (03) :811-814
[24]   NEW LOCALIZATION IN A QUASIPERIODIC SYSTEM [J].
HIRAMOTO, H ;
KOHMOTO, M .
PHYSICAL REVIEW LETTERS, 1989, 62 (23) :2714-2717
[25]   ELECTRONIC SPECTRAL AND WAVE-FUNCTION PROPERTIES OF ONE-DIMENSIONAL QUASI-PERIODIC SYSTEMS - A SCALING APPROACH [J].
HIRAMOTO, H ;
KOHMOTO, M .
INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 1992, 6 (3-4) :281-320
[26]   STUDIES OF POLARON MOTION .1. THE MOLECULAR-CRYSTAL MODEL [J].
HOLSTEIN, T .
ANNALS OF PHYSICS, 1959, 8 (03) :325-342
[27]  
Janner A., 1982, Europhysics News, V13, P1
[28]   MOBILITY EDGES AND MULTIFRACTAL PROPERTIES IN A ONE-DIMENSIONAL SYSTEM WITH 3 INCOMMENSURATE FREQUENCIES [J].
JOHANSSON, M ;
RIKLUND, R .
PHYSICAL REVIEW B, 1990, 42 (13) :8244-8254
[29]   NONLINEAR OPTICAL-RESPONSE OF SUPERLATTICES - MULTISTABILITY AND SOLITON TRAINS [J].
KAHN, L ;
ALMEIDA, NS ;
MILLS, DL .
PHYSICAL REVIEW B, 1988, 37 (14) :8072-8081
[30]   COMPARISON OF NONLINEAR OPTICAL-RESPONSES OF PERIODIC AND QUASIPERIODIC SUPERLATTICES [J].
KAHN, LM ;
HUANG, K ;
MILLS, DL .
PHYSICAL REVIEW B, 1989, 39 (17) :12449-12455