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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Institute of Physics Publishing
2018
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iium-676712019-04-10T07:45:32Z http://irep.iium.edu.my/67671/ Introduction to nonlinear discrete systems: theory and modelling Tsoy, Eduard N. Umarov, Bakhram A. QA297 Numerical Analysis QC Physics 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. Institute of Physics Publishing 2018-07-06 Article PeerReviewed application/pdf en http://irep.iium.edu.my/67671/20/67671_Measurement%20of%20differential%20cross%20sections_article.pdf application/pdf en http://irep.iium.edu.my/67671/7/67671_Introduction%20to%20nonlinear%20discrete%20systems_scopus.pdf application/pdf en http://irep.iium.edu.my/67671/14/67671_Introduction%20to%20nonlinear%20discrete.WOS.pdf Tsoy, Eduard N. and Umarov, Bakhram A. (2018) Introduction to nonlinear discrete systems: theory and modelling. European Journal of Physics, 39 (5). pp. 1-13. ISSN 0143-0807 E-ISSN 1361-6404 http://iopscience.iop.org/article/10.1088/1361-6404/aacca8/pdf 10.1088/1361-6404/aacca8 |
| repository_type |
Digital Repository |
| institution_category |
Local University |
| institution |
International Islamic University Malaysia |
| building |
IIUM Repository |
| collection |
Online Access |
| language |
English English English |
| topic |
QA297 Numerical Analysis QC Physics |
| spellingShingle |
QA297 Numerical Analysis QC Physics Tsoy, Eduard N. Umarov, Bakhram A. Introduction to nonlinear discrete systems: theory and modelling |
| description |
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. |
| format |
Article |
| author |
Tsoy, Eduard N. Umarov, Bakhram A. |
| author_facet |
Tsoy, Eduard N. Umarov, Bakhram A. |
| author_sort |
Tsoy, Eduard N. |
| title |
Introduction to nonlinear discrete systems:
theory and modelling |
| title_short |
Introduction to nonlinear discrete systems:
theory and modelling |
| title_full |
Introduction to nonlinear discrete systems:
theory and modelling |
| title_fullStr |
Introduction to nonlinear discrete systems:
theory and modelling |
| title_full_unstemmed |
Introduction to nonlinear discrete systems:
theory and modelling |
| title_sort |
introduction to nonlinear discrete systems:
theory and modelling |
| publisher |
Institute of Physics Publishing |
| publishDate |
2018 |
| url |
http://irep.iium.edu.my/67671/ http://irep.iium.edu.my/67671/ http://irep.iium.edu.my/67671/ 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 |
| first_indexed |
2023-09-18T21:36:03Z |
| last_indexed |
2023-09-18T21:36:03Z |
| _version_ |
1777412827707867136 |