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Symmetry
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Advances in Nonlinear, Discrete, Continuous and Hamiltonian Systems II
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Advances in Nonlinear, Discrete, Continuous and Hamiltonian Systems II

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

Deadline for manuscript submissions: closed (31 March 2023) | Viewed by 5948

Special Issue Editor

Prof. Dr. Miguel Ángel López Guerrero

E-Mail Website
Guest Editor
Polytechnic School of Cuenca, Department of Mathematics, University of Castilla-La Mancha, 16071 Cuenca, Spain
Interests: dynamical systems; numerical algorithms; nonlinear systems; applied mathematics; differential equations
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue is devoted to the dynamics of nonlinear systems in all their forms: discrete systems, continuous systems, and Hamiltonian systems. Topological dynamics tools, iterative methods, averaging approaches, and celestial mechanics ones are all suitable. The applications of these systems to information sciences, engineering, and mechanical problems are welcome. Moreover, systems modeling chemical graph theory, and biomedical or pharmacological performances are very welcome as well to this Special Issue.

Please note that all submitted papers must be within the general scope of the Symmetry journal.

Prof. MIGUEL ÁNGEL LÓPEZ GUERRERO
Guest Editor

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 systems discrete
  • continuous and Hamiltonian systems
  • iterative methods algorithms
  • symmetry

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Published Papers (3 papers)

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Research

16 pages, 455 KiB  
Article
The Convergence of Symmetric Discretization Models for Nonlinear Schrödinger Equation in Dark Solitons’ Motion
by Yazhuo Li, Qian Luo and Quandong Feng
Symmetry 2023, 15(6), 1229; https://doi.org/10.3390/sym15061229 - 9 Jun 2023
Cited by 1 | Viewed by 925
Abstract
The Schrödinger equation is one of the most basic equations in quantum mechanics. In this paper, we study the convergence of symmetric discretization models for the nonlinear Schrödinger equation in dark solitons’ motion and verify the theoretical results through numerical experiments. Via the [...] Read more.
The Schrödinger equation is one of the most basic equations in quantum mechanics. In this paper, we study the convergence of symmetric discretization models for the nonlinear Schrödinger equation in dark solitons’ motion and verify the theoretical results through numerical experiments. Via the second-order symmetric difference, we can obtain two popular space-symmetric discretization models of the nonlinear Schrödinger equation in dark solitons’ motion: the direct-discrete model and the Ablowitz–Ladik model. Furthermore, applying the midpoint scheme with symmetry to the space discretization models, we obtain two time–space discretization models: the Crank–Nicolson method and the new difference method. Secondly, we demonstrate that the solutions of the two space-symmetric discretization models converge to the solution of the nonlinear Schrödinger equation. Additionally, we prove that the convergence order of the two time–space discretization models is O(h2+τ2) in discrete L2-norm error estimates. Finally, we present some numerical experiments to verify the theoretical results and show that our numerical experiments agree well with the proven theoretical results. Full article
(This article belongs to the Special Issue Advances in Nonlinear, Discrete, Continuous and Hamiltonian Systems II)
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17 pages, 329 KiB  
Article
Linear Bundle of Lie Algebras Applied to the Classification of Real Lie Algebras
by Alina Dobrogowska and Karolina Wojciechowicz
Symmetry 2021, 13(8), 1455; https://doi.org/10.3390/sym13081455 - 9 Aug 2021
Cited by 2 | Viewed by 2043
Abstract
We present a new look at the classification of real low-dimensional Lie algebras based on the notion of a linear bundle of Lie algebras. Belonging to a suitable family of Lie bundles entails the compatibility of the Lie–Poisson structures with the dual spaces [...] Read more.
We present a new look at the classification of real low-dimensional Lie algebras based on the notion of a linear bundle of Lie algebras. Belonging to a suitable family of Lie bundles entails the compatibility of the Lie–Poisson structures with the dual spaces of those algebras. This gives compatibility of bi-Hamiltonian structure on the space of upper triangular matrices and with a bundle at the algebra level. We will show that all three-dimensional Lie algebras belong to two of these families and four-dimensional Lie algebras can be divided in three of these families. Full article
(This article belongs to the Special Issue Advances in Nonlinear, Discrete, Continuous and Hamiltonian Systems II)
15 pages, 313 KiB  
Article
Domination in Join of Fuzzy Incidence Graphs Using Strong Pairs with Application in Trading System of Different Countries
by Irfan Nazeer, Tabasam Rashid, Muhammad Tanveer Hussain and Juan Luis García Guirao
Symmetry 2021, 13(7), 1279; https://doi.org/10.3390/sym13071279 - 16 Jul 2021
Cited by 12 | Viewed by 2040
Abstract
Fuzzy graphs (FGs), broadly known as fuzzy incidence graphs (FIGs), are an applicable and well-organized tool to epitomize and resolve multiple real-world problems in which ambiguous data and information are essential. In this article, we extend the idea of domination of FGs to [...] Read more.
Fuzzy graphs (FGs), broadly known as fuzzy incidence graphs (FIGs), are an applicable and well-organized tool to epitomize and resolve multiple real-world problems in which ambiguous data and information are essential. In this article, we extend the idea of domination of FGs to the FIG using strong pairs. An idea of strong pair dominating set and a strong pair domination number (SPDN) is explained with various examples. A theorem to compute SPDN for a complete fuzzy incidence graph (CFIG) is also provided. It is also proved that in any fuzzy incidence cycle (FIC) with l vertices the minimum number of elements in a strong pair dominating set are M[γs(Cl(σ,ϕ,η))]=⌈l3⌉. We define the joining of two FIGs and present a way to compute SPDN in the join of FIGs. A theorem to calculate SPDN in the joining of two strong fuzzy incidence graphs is also provided. An innovative idea of accurate domination of FIGs is also proposed. Some instrumental and useful results of accurate domination for FIC are also obtained. In the end, a real-life application of SPDN to find which country/countries has/have the best trade policies among different countries is examined. Our proposed method is symmetrical to the optimization. Full article
(This article belongs to the Special Issue Advances in Nonlinear, Discrete, Continuous and Hamiltonian Systems II)
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