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Mathematics
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Mathematical Modelling of Wave Phenomena
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Mathematical Modelling of Wave Phenomena

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

Deadline for manuscript submissions: closed (30 November 2023) | Viewed by 1299

Special Issue Editors

Dr. Sergey A. Vakulenko

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Guest Editor
Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, Saint Petersburg 199178, Russia
Interests: nonlinear waves and patterns; chaotic dynamics; modelling of morphogenesis and evolution
Prof. Dr. Ovidiu Radulescu

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Guest Editor
Laboratory of Pathogens and Host Immunity, UMR CNRS 5294, University of Montpellier, 34095 Montpellier, France
Interests: systems biology; mathematical biology; dynamical systems; stochastic processes; condensed matter physics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue deals with the problems of mathematical modeling of nonlinear wave phenomena.  We focus on applications such as waves in ecology and biology, morphogenesis—in particular, somitogenesis—and waves in neuroscience.  We also consider waves in elastic systems with dissipative and diffusion effects.

In this Special Issue, to describe these wave phenomena, nonlinear parabolic equations, reaction–diffusion systems and nonlinear hyperbolic wave equations will be considered.

Dr. Sergey A. Vakulenko
Prof. Dr. Ovidiu Radulescu
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.

Published Papers (2 papers)

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Research

16 pages, 386 KiB  
Article
Meeting of Chemical Wave Fronts Creates Chaos
by Sergey Vakulenko and Alexander Galper
Mathematics 2024, 12(3), 429; https://doi.org/10.3390/math12030429 - 29 Jan 2024
Viewed by 482
Abstract
We consider systems of reaction–diffusion equations. We describe a new effect in the wave interaction for these systems: the collision of several travelling fronts may induce chaos or periodic oscillations. This effect depends on the initial locations of the travelling fronts: For some [...] Read more.
We consider systems of reaction–diffusion equations. We describe a new effect in the wave interaction for these systems: the collision of several travelling fronts may induce chaos or periodic oscillations. This effect depends on the initial locations of the travelling fronts: For some initial positions chaos occurs and for others it does not. In a space-homogeneous system, we need at least three fronts to create time-periodic behaviour, while to create chaos, we should have four fronts. We also provide a short review of previously known results, and different known mechanisms of chaos generation for reaction–diffusion systems. Our results can be used for pattern coding, in particular, for morphogenesis. Full article
(This article belongs to the Special Issue Mathematical Modelling of Wave Phenomena)
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11 pages, 313 KiB  
Article
Calculation of Sommerfeld Integrals in Dipole Radiation Problems
by Seil Sautbekov, Merey Sautbekova, Kuralay Baisalova and Mustakhim Pshikov
Mathematics 2024, 12(2), 298; https://doi.org/10.3390/math12020298 - 17 Jan 2024
Viewed by 562
Abstract
This article proposes asymptotic methods for calculating Sommerfeld integrals, which enable us to calculate the integral using the expansion of a function into an infinite power series at the saddle point, where the role of a rapidly oscillating function under the integral can [...] Read more.
This article proposes asymptotic methods for calculating Sommerfeld integrals, which enable us to calculate the integral using the expansion of a function into an infinite power series at the saddle point, where the role of a rapidly oscillating function under the integral can be fulfilled either by an exponential or by its product by the Hankel function. The proposed types of Sommerfeld integrals are generalized on the basis of integral representations of the Hertz radiator fields in the form of the inverse Hankel transform with the subsequent replacement of the Bessel function by the Hankel function. It is shown that the numerical values of the saddle point are complex. During integration, reference or so-called standard integrals, which contain the main features of the integrand function, were used. As a demonstration of the accuracy of the technique, a previously known asymptotic formula for the Hankel functions was obtained in the form of an infinite series. The proposed method for calculating Sommerfeld integrals can be useful in solving the half-space Sommerfeld problem. The authors present an example in the form of an infinite series for the magnetic field of reflected waves, obtained directly through the Sommerfeld integral (SI). Full article
(This article belongs to the Special Issue Mathematical Modelling of Wave Phenomena)
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