Introduction to nonlinear discrete systems: theory and modelling
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 proper...
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| Main Authors: | , |
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| Format: | Article |
| Language: | en en en |
| Published: |
Institute of Physics Publishing
2018
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/67671/20/67671_Measurement%20of%20differential%20cross%20sections_article.pdf http://irep.iium.edu.my/67671/7/67671_Introduction%20to%20nonlinear%20discrete%20systems_scopus.pdf http://irep.iium.edu.my/67671/14/67671_Introduction%20to%20nonlinear%20discrete.WOS.pdf http://irep.iium.edu.my/67671/ http://iopscience.iop.org/article/10.1088/1361-6404/aacca8/pdf |
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| Summary: | 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
Schrödinger (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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