Symmetries in Differential Equations and Application - Volume II

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

Deadline for manuscript submissions: 30 September 2024 | Viewed by 975

Special Issue Editor


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Guest Editor
Department of Mathematics, Hannam University, Daejeon 34430, Republic of Korea
Interests: numerical verification method; scientific computing; differential equations; dynamical systems; quantum calculus and special functions
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Special Issue Information

Dear Colleagues,

The study of differential equations is a wide field in pure and applied mathematics. All of these fields relate to the properties of various types of differential equations.

Pure mathematics investigates the existence and uniqueness of solutions, while applied mathematics enforces a strict justification of how to approximate solutions.

Differential equations play a significant role in modeling virtually every physical, technical and biological process. These areas remain at the center of advanced mathematical research. Differential equations, such as those employed in order to solve real problems, are not necessarily directly solvable. Instead, solutions can be approximated using numerical methods. These methods are pivotal to studies in advanced mathematics, physics, and engineering, with many potential applications. Recently, differential equations have been closely related to several areas in mathematics, applied mathematics, physics, chemistry, biological sciences, and engineering, and have been employed to share recent knowledge and research in pure, as well as applied, mathematical sciences.

This Special Issue aims to publish major research papers and present the latest trends in pure and applied mathematical sciences, including the area of differential equations.

Prof. Dr. Cheon-Seoung Ryoo
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

  • differential equation
  • symmetry
  • pseudo-differential operator
  • numerical analysis
  • approximation
  • a priori estimates
  • stability
  • asymptotic properties
  • numerical verification method
  • dynamical systems
  • quantum calculus
  • special functions

Published Papers (1 paper)

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Research

12 pages, 269 KiB  
Article
Non-Classical Symmetry Analysis of a Class of Nonlinear Lattice Equations
by Wenting Li, Yueting Chen and Kun Jiang
Symmetry 2023, 15(12), 2199; https://0-doi-org.brum.beds.ac.uk/10.3390/sym15122199 - 14 Dec 2023
Viewed by 706
Abstract
In this paper, a non-classical symmetry method for obtaining the symmetries of differential–difference equations is proposed. The non-classical symmetry method introduces an additional constraint known as the invariant surface condition, which is applied after the infinitesimal transformation. By solving the governing equations that [...] Read more.
In this paper, a non-classical symmetry method for obtaining the symmetries of differential–difference equations is proposed. The non-classical symmetry method introduces an additional constraint known as the invariant surface condition, which is applied after the infinitesimal transformation. By solving the governing equations that satisfy this condition, we can obtain the corresponding reduced equation. This allows us to determine the non-classical symmetry of the differential–difference equation. This method avoids the complicated calculation involved in extending the infinitesimal generator and allows for a wider range of symmetry forms. As a result, it enables the derivation of a greater number of differential–difference equations. In this paper, two kinds of (2+1)-dimensional Toda-like lattice equations are taken as examples, and their corresponding symmetric and reduced equations are obtained using the non-classical symmetry method. Full article
(This article belongs to the Special Issue Symmetries in Differential Equations and Application - Volume II)
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