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Mathematical and Numerical Analysis of Nonlinear Evolution Equations: Advances and...
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Mathematical and Numerical Analysis of Nonlinear Evolution Equations: Advances and Perspectives, 2nd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E4: Mathematical Physics".

Deadline for manuscript submissions: 30 September 2025 | Viewed by 3173

Special Issue Editor

Prof. Dr. Carlo Bianca

E-Mail Website
Guest Editor
Department of Mathematics, EFrei Research Lab, Paris-Panthéon-Assas University, 30/32 Avenue de la République, 94800 Villejuif, France
Interests: mathematical modeling and analysis of complex systems; kinetic equations; numerical methods for PDE
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Recently, interactions between researchers working in the fields of mathematical physics and applied sciences have gained much attention, and new challenges have been raised, including the possibility of deriving evolution differential equations that are able to describe most phenomena arising in real-world systems. On one hand, mathematical analysis allows us to obtain information regarding the qualitative behaviors of the system including the existence of solutions, asymptotic behaviors, and nonlinear dynamics. On the other hand, numerical and computational analysis furnishes methods to obtain quantitative information about solutions and the possibility of comparing the time evolution of solutions to differential equations with empirical data.

This Special Issue is devoted to researchers working in the fields of pure and applied mathematical physics, specifically to researchers who are involved in the mathematical and numerical analysis of nonlinear evolution equations and their applications. Original research articles and review articles are welcome.

The topics include, but are not limited to, the following:

  • Prey–predator models;
  • Kinetic-type models;
  • Multiscale models;
  • Computational models;
  • Fractional models;
  • Asymptotic analysis and methods;
  • Approximative methods;
  • Bifurcation analysis;
  • Chaos and synchronization analysis;
  • Nonlinear dynamics;
  • Complex dynamics;
  • Far-from-equilibrium dynamics;
  • Blow-up of solutions;
  • Fractional calculus.

Prof. Dr. Carlo Bianca
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. 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.

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Related Special Issue

Published Papers (3 papers)

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18 pages, 5088 KiB  
Article
Dynamical Visualization and Qualitative Analysis of the (4+1)-Dimensional KdV-CBS Equation Using Lie Symmetry Analysis
by Maria Luz Gandarias, Nauman Raza, Muhammad Umair and Yahya Almalki
Mathematics 2025, 13(1), 89; https://doi.org/10.3390/math13010089 - 29 Dec 2024
Cited by 1 | Viewed by 732
Abstract
This study investigates novel optical solitons within the intriguing (4+1)-dimensional Korteweg–de Vries–Calogero–Bogoyavlenskii–Schiff (KdV-CBS) equation, which integrates features from both the Korteweg–de Vries and the Calogero–Bogoyavlenskii–Schiff equations. Firstly, all possible symmetry generators are found by applying Lie symmetry analysis. By using these generators, the [...] Read more.
This study investigates novel optical solitons within the intriguing (4+1)-dimensional Korteweg–de Vries–Calogero–Bogoyavlenskii–Schiff (KdV-CBS) equation, which integrates features from both the Korteweg–de Vries and the Calogero–Bogoyavlenskii–Schiff equations. Firstly, all possible symmetry generators are found by applying Lie symmetry analysis. By using these generators, the given model is converted into an ordinary differential equation. An adaptive approach, the generalized exp(-S(χ)) expansion technique has been utilized to uncover closed-form solitary wave solutions. The findings reveal a range of soliton types, including exponential, rational, hyperbolic, and trigonometric functions, represented as bright, singular, rational, periodic, and new solitary waves. These results are illustrated numerically and accompanied by insightful physical interpretations, enriching the comprehension of the complex dynamics modeled by these equations. Our approach’s novelty lies in applying a new methodology to this problem, yielding a variety of novel optical soliton solutions. Additionally, we employ bifurcation and chaos techniques for a qualitative analysis of the model, extracting a planar system from the original equation and mapping all possible phase portraits. A thorough sensitivity analysis of the governing equation is also presented. These results highlight the effectiveness of our methodology in tackling nonlinear problems in both mathematics and engineering, surpassing previous research efforts. Full article
(This article belongs to the Special Issue Mathematical and Numerical Analysis of Nonlinear Evolution Equations: Advances and Perspectives, 2nd Edition)
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12 pages, 341 KiB  
Article
Dynamics of a Price Adjustment Model with Distributed Delay
by Luca Guerrini, Martin Anokye, Albert L. Sackitey and John Amoah-Mensah
Mathematics 2024, 12(20), 3220; https://doi.org/10.3390/math12203220 - 14 Oct 2024
Viewed by 799
Abstract
This paper deals with the stability and occurrence of Hopf bifurcation of a distributed delay differential cobweb model using the chain trick technique. This is a generalized form of the fixed delay cobweb model to which it is compared using the same parameter [...] Read more.
This paper deals with the stability and occurrence of Hopf bifurcation of a distributed delay differential cobweb model using the chain trick technique. This is a generalized form of the fixed delay cobweb model to which it is compared using the same parameter values. The results from the delay distribution showed that whenever less weight (γ=0.146) is put on past prices, the current equilibrium price is adjusted upwards while the reverse is observed when a higher weight (γ=0.186) is put on the previous price. It is also observed that if the initial price is set below/above the equilibrium price, the price adjustment either affects the consumers or benefits the suppliers. However, the fixed delay cobweb model does not display the consumers or suppliers benefits of the price dynamics in either direction. These are unique, underlying patterns in price dynamics discovered when using a distributed delay model compared to traditional fixed delay cobweb models. Furthermore, our model challenges the traditional cobweb model’s requirement for divergence, as it is based on the weight assigned to past prices rather than the relationship between the elasticities of supply and demand, which is the determining factor in the classical model. Based on these insights, we recommend that future price adjustment models incorporate distributed delays, as they reveal more intricate price dynamics and provide a more comprehensive understanding of market behavior than fixed delay models. Full article
(This article belongs to the Special Issue Mathematical and Numerical Analysis of Nonlinear Evolution Equations: Advances and Perspectives, 2nd Edition)
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20 pages, 352 KiB  
Article
The Role of the Table of Games in the Discrete Thermostatted Kinetic Theory
by Carlo Bianca
Mathematics 2024, 12(15), 2356; https://doi.org/10.3390/math12152356 - 28 Jul 2024
Viewed by 1019
Abstract
This paper is concerned with the mathematical modeling of complex living systems whose element microscopic state contains variables which can attain discrete values. Specifically, the main mathematical frameworks of the discrete thermostatted kinetic theory for active particles are reviewed and generalized. In the [...] Read more.
This paper is concerned with the mathematical modeling of complex living systems whose element microscopic state contains variables which can attain discrete values. Specifically, the main mathematical frameworks of the discrete thermostatted kinetic theory for active particles are reviewed and generalized. In the generalized thermostatted frameworks, which are based on nonlinear ordinary or partial differential equations, the elements of the system are viewed as active particles that are able to perform certain strategies modeled by introducing a functional-state variable called activity. Interactions, which are responsible of the evolution of the system, are modeled using the fundamentals of stochastic game theory and may be influenced by the action of an external force field coupled to a Gaussian-type thermostat. In particular, the interaction domain is modeled by introducing a weighted function and different non-homogeneous discrete frameworks are proposed and coupled with a specific thermostat. Two recent models derived within this approach are reviewed and refer to vehicular and pedestrian dynamics. Future research perspectives are discussed in the whole paper from theoretical and modeling viewpoints. Full article
(This article belongs to the Special Issue Mathematical and Numerical Analysis of Nonlinear Evolution Equations: Advances and Perspectives, 2nd Edition)
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