Exact Solutions and Numerical Solutions of Differential Equations

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".

Deadline for manuscript submissions: 31 December 2024 | Viewed by 3144

Special Issue Editors


E-Mail Website
Guest Editor
1. Department of Mathematics, Faculty of Science, University of Botswana, Private Bag 22, Gaborone, Botswana
2. Department of Mathematical Sciences, North-West University, Private Bag X 2046, Mmabatho 2735, South Africa
Interests: symmetries of differentials equations; soliton theory

E-Mail Website
Guest Editor
Department of Mathematical Sciences, University of South Africa, UNISA, Pretoria 0003, South Africa
Interests: conservation laws of partial differentials equations; mathematical physics
Department of Mathematics, University of Botswana, Private Bag UB00704, Gaborone, Botswana
Interests: numerical analysis; monotone nonlinear equations; optimization

Special Issue Information

Dear Colleagues,

Nonlinear differential equations play a significant role in many real-life phenomena, such as in fluid dynamics, optics, acoustics, plasma physics, engineering, and in many other areas of nonlinear science. Thus, it is incredibly vital to find solutions to these equations in order to understand and interpret the structure modeled by these equations.

However, researchers have developed a variety of analytical and numerical techniques that can be employed to solve nonlinear differential equations. Some of the well-known techniques include the Lie symmetry method, the inverse scattering transformation approach, Ansatz methods, multistep methods, finite difference/element/volume methods, and many other techniques in the literature.

This Special Issue will be devoted to unveiling the most recent progress in obtaining analytical and numerical solutions to nonlinear differential equations via various methods and to stimulating collaborative research activities. 

Dr. Ben Muatjetjeja
Prof. Dr. Abdullahi Adem
Dr. P. Kaelo
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

  • symmetries of differentials equations
  • soliton theory conservation laws of partial differentials equations
  • mathematical physics
  • numerical analysis
  • monotone nonlinear equations

Published Papers (4 papers)

Order results
Result details
Select all
Export citation of selected articles as:

Research

10 pages, 1597 KiB  
Article
Analyzing Soliton Solutions of the Extended (3 + 1)-Dimensional Sakovich Equation
by Rubayyi T. Alqahtani and Melike Kaplan
Mathematics 2024, 12(5), 720; https://doi.org/10.3390/math12050720 - 29 Feb 2024
Viewed by 524
Abstract
This work focuses on the utilization of the generalized exponential rational function method (GERFM) to analyze wave propagation of the extended (3 + 1)-dimensional Sakovich equation. The demonstrated effectiveness and robustness of the employed method underscore its relevance to a wider spectrum of [...] Read more.
This work focuses on the utilization of the generalized exponential rational function method (GERFM) to analyze wave propagation of the extended (3 + 1)-dimensional Sakovich equation. The demonstrated effectiveness and robustness of the employed method underscore its relevance to a wider spectrum of nonlinear partial differential equations (NPDEs) in physical phenomena. An examination of the physical characteristics of the generated solutions has been conducted through two- and three-dimensional graphical representations. Full article
(This article belongs to the Special Issue Exact Solutions and Numerical Solutions of Differential Equations)
Show Figures

Figure 1

13 pages, 555 KiB  
Article
Simulation of a Combined (2+1)-Dimensional Potential Kadomtsev–Petviashvili Equation via Two Different Methods
by Muath Awadalla, Arzu Akbulut and Jihan Alahmadi
Mathematics 2024, 12(3), 427; https://doi.org/10.3390/math12030427 - 29 Jan 2024
Viewed by 488
Abstract
This paper presents an investigation into original analytical solutions of the (2+1)-dimensional combined potential Kadomtsev–Petviashvili and B-type Kadomtsev–Petviashvili equations. For this purpose, the generalized Kudryashov technique (GKT) and exponential rational function technique (ERFT) have been applied to deal with the equation. These two [...] Read more.
This paper presents an investigation into original analytical solutions of the (2+1)-dimensional combined potential Kadomtsev–Petviashvili and B-type Kadomtsev–Petviashvili equations. For this purpose, the generalized Kudryashov technique (GKT) and exponential rational function technique (ERFT) have been applied to deal with the equation. These two methods have been applied to the model for the first time, and the the generalized Kudryashov method has an important place in the literature. The characteristics of solitons are unveiled through the use of three-dimensional, two-dimensional, contour, and density plots. Furthermore, we conducted a stability analysis on the acquired results. The results obtained in the article were seen to be different compared to other results in the literature and have not been published anywhere before. Full article
(This article belongs to the Special Issue Exact Solutions and Numerical Solutions of Differential Equations)
Show Figures

Figure 1

12 pages, 901 KiB  
Article
On the Dynamics of the Complex Hirota-Dynamical Model
by Arzu Akbulut, Melike Kaplan, Rubayyi T. Alqahtani and W. Eltayeb Ahmed
Mathematics 2023, 11(23), 4851; https://doi.org/10.3390/math11234851 - 02 Dec 2023
Viewed by 682
Abstract
The complex Hirota-dynamical Model (HDM) finds multifarious applications in fields such as plasma physics, fusion energy exploration, astrophysical investigations, and space studies. This study utilizes several soliton-type solutions to HDM via the modified simple equation and generalized and modified Kudryashov approaches. Modulation instability [...] Read more.
The complex Hirota-dynamical Model (HDM) finds multifarious applications in fields such as plasma physics, fusion energy exploration, astrophysical investigations, and space studies. This study utilizes several soliton-type solutions to HDM via the modified simple equation and generalized and modified Kudryashov approaches. Modulation instability (MI) analysis is investigated. We also offer visual representations for the HDM. Full article
(This article belongs to the Special Issue Exact Solutions and Numerical Solutions of Differential Equations)
Show Figures

Figure 1

11 pages, 1073 KiB  
Article
New (3+1)-Dimensional Kadomtsev–Petviashvili–Sawada– Kotera–Ramani Equation: Multiple-Soliton and Lump Solutions
by Abdul-Majid Wazwaz, Ma’mon Abu Hammad, Ali O. Al-Ghamdi, Mansoor H. Alshehri and Samir A. El-Tantawy
Mathematics 2023, 11(15), 3395; https://doi.org/10.3390/math11153395 - 03 Aug 2023
Cited by 4 | Viewed by 935
Abstract
In this investigation, a novel (3+1)-dimensional Lax integrable Kadomtsev–Petviashvili–Sawada–Kotera–Ramani equation is constructed and analyzed analytically. The Painlevé integrability for the mentioned model is examined. The bilinear form is applied for investigating multiple-soliton solutions. Moreover, we employ the positive quadratic function method to create [...] Read more.
In this investigation, a novel (3+1)-dimensional Lax integrable Kadomtsev–Petviashvili–Sawada–Kotera–Ramani equation is constructed and analyzed analytically. The Painlevé integrability for the mentioned model is examined. The bilinear form is applied for investigating multiple-soliton solutions. Moreover, we employ the positive quadratic function method to create a class of lump solutions using distinct parameters values. The current study serves as a guide to explain many nonlinear phenomena that arise in numerous scientific domains, such as fluid mechanics; physics of plasmas, oceans, and seas; and so on. Full article
(This article belongs to the Special Issue Exact Solutions and Numerical Solutions of Differential Equations)
Show Figures

Figure 1

Back to TopTop