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Mathematics
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Symmetry Methods and Applications for Nonlinear Partial Differential Equations II
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Symmetry Methods and Applications for Nonlinear Partial Differential Equations II

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: closed (10 October 2023) | Viewed by 2759

Special Issue Editors

Prof. Dr. Maria Luz Gandarias

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Guest Editor
Department of Mathematics, Cádiz University, 11003 Cádiz, Spain
Interests: symmetry methods; applications for differential equations
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Maria Rosa

E-Mail Website
Guest Editor
Departamento de Matemáticas, University of Cádiz, Puerto Real, 11003 Cádiz, Spain
Interests: numerical analysis; mathematical modeling; partial differential equations; mathematical oncology
Special Issues, Collections and Topics in MDPI journals
Dr. Rita Tracinà

E-Mail Website
Guest Editor
Department of Mathematics and Computer Science, Catania University, 95125 Catania, Italy
Interests: symmetry methods; applications for differential equations
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Many real-world problems which arise in various scientific fields, such as economics, biology, physics, fluid dynamics, and engineering, are modeled by physically and mathematically interesting nonlinear differential partial equations (PDEs). To study the exact properties of such equations, symmetries and conservation laws are powerful tools that can provide explicit solutions, conserved quantities, transformations to simpler equations, tests of numerical schemes, and more.

The aim of this Special Issue is to focus on recent developments in symmetry analysis and conservation law analysis with applications to nonlinear PDEs of physical interest.

Other approaches in finding exact solutions to nonlinear differential equations will also be welcomed. High-quality papers that contain original research results are encouraged.

Prof. Dr. Maria Luz Gandarias
Prof. Dr. Maria Rosa
Dr. Rita Tracinà
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • symmetry groups
  • conservation laws
  • partial differential equations

Published Papers (2 papers)

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Research

13 pages, 4886 KiB  
Article
A Radial Basis Scale Conjugate Gradient Deep Neural Network for the Monkeypox Transmission System
by Zulqurnain Sabir, Salem Ben Said and Juan L. G. Guirao
Mathematics 2023, 11(4), 975; https://doi.org/10.3390/math11040975 - 15 Feb 2023
Cited by 6 | Viewed by 1088
Abstract
The motive of this study is to provide the numerical performances of the monkeypox transmission system (MTS) by applying the novel stochastic procedure based on the radial basis scale conjugate gradient deep neural network (RB-SCGDNN). Twelve and twenty numbers of neurons were taken [...] Read more.
The motive of this study is to provide the numerical performances of the monkeypox transmission system (MTS) by applying the novel stochastic procedure based on the radial basis scale conjugate gradient deep neural network (RB-SCGDNN). Twelve and twenty numbers of neurons were taken in the deep neural network process in first and second hidden layers. The MTS dynamics were divided into rodent and human, the human was further categorized into susceptible, infectious, exposed, clinically ill, and recovered, whereas the rodent was classified into susceptible, infected, and exposed. The construction of dataset was provided through the Adams method that was refined further by using the training, validation, and testing process with the statics of 0.15, 0.13 and 0.72. The exactness of the RB-SCGDNN is presented by using the comparison of proposed and reference results, which was further updated through the negligible absolute error and different statistical performances to solve the nonlinear MTS. Full article
(This article belongs to the Special Issue Symmetry Methods and Applications for Nonlinear Partial Differential Equations II)
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13 pages, 759 KiB  
Article
A Comprehensive Study of the Complex mKdV Equation through the Singular Manifold Method
by Paz Albares and Pilar G. Estévez
Mathematics 2023, 11(4), 859; https://doi.org/10.3390/math11040859 - 08 Feb 2023
Viewed by 1222
Abstract
In this paper, we introduce a modification of the Singular Manifold Method in order to derive the associated spectral problem for a generalization of the complex version of the modified Korteweg–de Vries equation. This modification yields the right Lax pair and allows us [...] Read more.
In this paper, we introduce a modification of the Singular Manifold Method in order to derive the associated spectral problem for a generalization of the complex version of the modified Korteweg–de Vries equation. This modification yields the right Lax pair and allows us to implement binary Darboux transformations, which can be used to construct an iterative method to obtain exact solutions. Full article
(This article belongs to the Special Issue Symmetry Methods and Applications for Nonlinear Partial Differential Equations II)
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