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Symmetry
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Advances in Nonlinear Dynamics and Symmetry
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Advances in Nonlinear Dynamics and Symmetry

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (31 December 2022) | Viewed by 9720

Special Issue Editors

Prof. Dr. Branko Dragovich

E-Mail Website
Guest Editor
1. Institute of Physics, University of Belgrade, Belgrade, Serbia
2. Mathematical Institute, Serbian Academy of Sciences and Arts, Belgrade, Serbia
Interests: modified gravity; cosmology; p-adic analysis; p-adic mathematical physics; p-adic string theory; genetic code and bioinformation
Special Issues, Collections and Topics in MDPI journals
Dr. Milivoj Belic

E-Mail Website
Guest Editor
Science Program, Texas A&M University at Qatar, Doha 23874, Qatar
Interests: nonlinear optics and nonlinear dynamics; condensed matter physics; numerical modeling of complex systems

Special Issue Information

Dear Colleagues,

Nonlinear phenomena are present everywhere and are investigated by many fundamental and applied sciences. Recent developments in various theoretical and applied aspects of nonlinear dynamics will be presented and discussed at the “2nd Conference on Nonlinearity”, http://www.nonlinearity2021.matf.bg.ac.rs/, organized by the Serbian Academy of Nonlinear Sciences, http://www.sann.kg.ac.rs/en/sans/, to be held on 18–22 October 2021 in Belgrade, Serbia. The goal of this Special Issue is to present a collection of recent advances in nonlinear dynamics, its symmetries, theoretical modeling and applications. The plan is to present selected contributions to the “2nd Conference on Nonlinearity”, in addition to other significant submissions sent directly to the Editors.

Prof. Dr. Branko Dragovich
Dr. Milivoj Belic
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • nonlinear dynamics
  • nonlinear optics
  • nonlinear differential equations
  • nonlinear phenomena
  • nonlinear methods
  • nonlinear sciences
  • nonlinearity

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Published Papers (3 papers)

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Research

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16 pages, 519 KiB  
Article
Algebraic Analysis of Zero-Hopf Bifurcation in a Chua System
by Bo Huang, Wei Niu and Shaofen Xie
Symmetry 2022, 14(5), 1036; https://doi.org/10.3390/sym14051036 - 18 May 2022
Cited by 1 | Viewed by 1526
Abstract
This article first studies the stability conditions of a Chua system depending on six parameters. After, using the averaging method, as well as the methods of the Gröbner basis and real solution classification, we provide sufficient conditions for the existence of three limit [...] Read more.
This article first studies the stability conditions of a Chua system depending on six parameters. After, using the averaging method, as well as the methods of the Gröbner basis and real solution classification, we provide sufficient conditions for the existence of three limit cycles bifurcating from a zero-Hopf equilibrium of the Chua system. As we know, this last phenomena is first found. Some examples are presented to verify the established results. Full article
(This article belongs to the Special Issue Advances in Nonlinear Dynamics and Symmetry)
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17 pages, 713 KiB  
Article
The Functional Expansion Approach for Solving NPDEs as a Generalization of the Kudryashov and G′/G Methods
by Carmen Ionescu, Corina N. Babalic, Radu Constantinescu and Raluca Efrem
Symmetry 2022, 14(4), 827; https://doi.org/10.3390/sym14040827 - 15 Apr 2022
Cited by 5 | Viewed by 2001
Abstract
This paper presents the functional expansion approach as a generalized method for finding traveling wave solutions of various nonlinear partial differential equations. The approach can be seen as a combination of the Kudryashov and G′/G solving methods. It allowed the [...] Read more.
This paper presents the functional expansion approach as a generalized method for finding traveling wave solutions of various nonlinear partial differential equations. The approach can be seen as a combination of the Kudryashov and G′/G solving methods. It allowed the extension of the first method to the use of second order auxiliary equations, and, at the same time, it allowed non-standard G′/G-solutions to be generated. The functional expansion is illustrated here on the Dodd–Bullough–Mikhailov model, using a linear second order ordinary differential equation as an auxiliary equation. Full article
(This article belongs to the Special Issue Advances in Nonlinear Dynamics and Symmetry)
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Review

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26 pages, 2285 KiB  
Review
Two-Dimensional Solitons in Nonlocal Media: A Brief Review
by Boris A. Malomed
Symmetry 2022, 14(8), 1565; https://doi.org/10.3390/sym14081565 - 29 Jul 2022
Cited by 29 | Viewed by 5369
Abstract
This is a review addressing soliton-like states in systems with nonlocal nonlinearity. The work on this topic has long history in optics and related areas. Some results produced by the work (such as solitons supported by thermal nonlinearity in optical glasses, and orientational [...] Read more.
This is a review addressing soliton-like states in systems with nonlocal nonlinearity. The work on this topic has long history in optics and related areas. Some results produced by the work (such as solitons supported by thermal nonlinearity in optical glasses, and orientational nonlinearity, which affects light propagation in liquid crystals) are well known, and have been properly reviewed in the literature, therefore the respective models are outlined in the present review in a brief form. Some other studies, such as those addressing models with fractional diffraction, which is represented by a linear nonlocal operator, have started more recently, therefore it will be relevant to review them in detail when more results will be accumulated; for this reason, the present article provides a short outline of the latter topic. The main part of the article is a summary of results obtained for two-dimensional solitons in specific nonlocal nonlinear models originating in studies of Bose–Einstein condensates (BECs), which are sufficiently mature but have not yet been reviewed previously (some results for three-dimensional solitons are briefly mentioned too). These are, in particular, anisotropic quasi-2D solitons supported by long-range dipole-dipole interactions in a condensate of magnetic atoms and giant vortex solitons (which are stable for high values of the winding number), as well as 2D vortex solitons of the latter type moving with self-acceleration. The vortex solitons are states of a hybrid type, which include matter-wave and electromagnetic-wave components. They are supported, in a binary BEC composed of two different atomic states, by the resonant interaction of the two-component matter waves with a microwave field that couples the two atomic states. The shape, stability, and dynamics of the solitons in such systems are strongly affected by their symmetry. Some other topics are included in the review in a brief form. This review uses the “Harvard style” of referring to the bibliography. Full article
(This article belongs to the Special Issue Advances in Nonlinear Dynamics and Symmetry)
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