期刊
EUROPEAN JOURNAL OF PHYSICS
卷 39, 期 5, 页码 -出版社
IOP Publishing Ltd
DOI: 10.1088/1361-6404/aacca8
关键词
discrete systems; lattices; arrays; chains; discrete nonlinear Schrodinger equation; discrete solitons; Mathematica code
资金
- Agency for Science and Technologies, Uzbekistan [FA-F2-004]
- Ministry of Higher Education, Malaysia [FRGS 16-014-0513]
An analysis of discrete systems is important for understanding of various physical processes, such as excitations in crystal lattices and molecular chains, the light propagation in waveguide arrays, and the dynamics of Bose-condensate droplets. In basic physical courses, usually the linear properties of discrete systems are studied. In this paper we propose a pedagogical introduction to the theory of nonlinear distributed systems. The main ideas and methods are illustrated using a universal model for different physical applications, the discrete nonlinear Schrodinger (DNLS) equation. We consider solutions of the DNLS equation and analyse their linear stability. The notions of nonlinear plane waves, modulational instability, discrete solitons and the anti-continuum limit are introduced and thoroughly discussed. A Mathematica program is provided for better comprehension of results and further exploration. Also, a few problems, extending the topic of the paper, for independent solution are given.
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