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Axioms
Special Issues
Nonlinear Dynamics and Complexity
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Nonlinear Dynamics and Complexity

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (30 April 2023) | Viewed by 4559

Special Issue Editors

Prof. Dr. Irina Papkova

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Guest Editor
Department of Mathematics and Modelling, Yuri Gagarin State Technical University of Saratov, Saratov, Russia
Interests: mathematical modeling; nonlinear analysis; dynamics; engineering, applied, and computational mathematics; signal processing; signal, image, and video processing; numerical modeling; structural dynamics; modeling and simulation; numerical analysis
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Tatyana Yakovleva

E-Mail Website
Guest Editor
Department of Mathematics and Modelling, Yuri Gagarin State Technical University of Saratov, Saratov, Russia
Interests: nonlinear analysis; dynamics; numerical modeling; structural dynamics; modeling and simulation; numerical analysis

Special Issue Information

Dear Colleagues,

This Special Issue is dedicated to mathematical and numerical modeling of various processes in mechanics, biomechanics, biology, chemistry, physics, and other fields. This book aims to cover various analytical and numerical methods in solving partial differential equations. Topics include mathematical models, differential equations systems solutions to the stability problem, and nonlinear dynamics problems of beam–plate–shell structures, in the form of both experimental studies and theoretical developments, taking into account deformation and fracture and contact interaction of structures. This issue is also devoted to the consideration and construction of mathematical models for nonlinear oscillations of biological structures, and physical, chemical, and mechanical processes, as well as the construction and substantiation of nonlinear analysis methods of micro- and nanomaterials.

The issue will undoubtedly serve as a valuable guide for researchers interested in participating in this interdisciplinary field. In addition, it will be useful for encouraging further experimental and theoretical research in the fields of numerical modeling mentioned above, which use mathematical and computer modeling.

Prof. Dr. Irina Papkova
Prof. Dr. Tatyana Yakovleva
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. Axioms 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

  • nonlinear dynamics
  • statics
  • stability
  • differential equations
  • methods for solving differential equations
  • numerical modeling of physical, chemical, mechanical, and biological processes

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Published Papers (2 papers)

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13 pages, 5827 KiB  
Article
Nonlinear Dynamic Behaviors of the (3+1)-Dimensional B-Type Kadomtsev—Petviashvili Equation in Fluid Mechanics
by Kang-Jia Wang, Jing-Hua Liu, Jing Si and Guo-Dong Wang
Axioms 2023, 12(1), 95; https://doi.org/10.3390/axioms12010095 - 16 Jan 2023
Cited by 16 | Viewed by 2370
Abstract
This paper provides an investigation on nonlinear dynamic behaviors of the (3+1)-dimensional B-type Kadomtsev—Petviashvili equation, which is used to model the propagation of weakly dispersive waves in a fluid. With the help of the Cole—Hopf transform, the Hirota bilinear equation is established, then [...] Read more.
This paper provides an investigation on nonlinear dynamic behaviors of the (3+1)-dimensional B-type Kadomtsev—Petviashvili equation, which is used to model the propagation of weakly dispersive waves in a fluid. With the help of the Cole—Hopf transform, the Hirota bilinear equation is established, then the symbolic computation with the ansatz function schemes is employed to search for the diverse exact solutions. Some new results such as the multi-wave complexiton, multi-wave, and periodic lump solutions are found. Furthermore, the abundant traveling wave solutions such as the dark wave, bright-dark wave, and singular periodic wave solutions are also constructed by applying the sub-equation method. Finally, the nonlinear dynamic behaviors of the solutions are presented through the 3-D plots, 2-D contours, and 2-D curves and their corresponding physical characteristics are also elaborated. To our knowledge, the obtained solutions in this work are all new, which are not reported elsewhere. The methods applied in this study can be used to investigate the other PDEs arising in physics. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Complexity)
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10 pages, 940 KiB  
Article
How Micelles Influence the Optical Limiting Properties of Zinc Porphyrins and J-Aggregates for Picosecond Pulse Trains
by Quan Miao, Erping Sun and Yan Xu
Axioms 2023, 12(1), 23; https://doi.org/10.3390/axioms12010023 - 25 Dec 2022
Viewed by 1514
Abstract
In this work, we studied nonlinear dynamics and optical limiting (OL) effects of pulse trains in zinc porphyrins meso-tetrakis methylpyridiniumyl (Zn2+TMPyP) and meso-tetrakis sulfonatophenyl (Zn2+TPPS) and porphyrin J-aggregates. The environments of zinc porphyrins were selected as aqueous [...] Read more.
In this work, we studied nonlinear dynamics and optical limiting (OL) effects of pulse trains in zinc porphyrins meso-tetrakis methylpyridiniumyl (Zn2+TMPyP) and meso-tetrakis sulfonatophenyl (Zn2+TPPS) and porphyrin J-aggregates. The environments of zinc porphyrins were selected as aqueous solutions and micelles of sodium dodecyl sulfate (SDS) and cetyltrimethyl ammonium bromide (CTAB). Our numerical results show that both Zn2+TMPyP and Zn2+TPPS are good optical limiters in all solutions. Zn2+TPPS in aqueous solutions shows the best OL effect. Micelles of SDS and CTAB produced less OL effects than the aqueous solutions. The main reason lies in the first excited singlet state and intersystem crossing depending on the electronic structures in different environments. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Complexity)
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