The Application of Mathematics to Physics and Nonlinear Science
A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematical Physics".
Deadline for manuscript submissions: closed (31 December 2019) | Viewed by 13152
Special Issue Editor
Interests: nonlinear fluid dynamics; drops; liquid bubbles; liquid shells; solitons and nonlinear waves on compact surfaces; extreme waves; patterns; liquid drop nuclear model; clusters; Leidenfrost effect
Special Issue Information
Dear Colleagues,
The importance of understanding nonlinearity has increased over the decades, through the development of newer fields of application: elementary particles, biophysics, wave dynamics, optical fibers, fluids, plasmas, social and ecological systems, astrophysics, and cross-disciplinary fields. The necessary mathematics involves nonlinear evolution equations. Obtaining closed-form solutions for these equations plays an important role in the proper understanding of features of many phenomena, by unraveling the mechanisms of complex phenomena such as pattern formation and selection, the spatial localization of transfer processes, the multiplicity or absence steady states under various conditions, the existence of peaking regimes, etc. Even exact test solutions with no immediate physical meaning are used to verify the consistency of numerical, asymptotic, and approximate analytical methods. In spite of various solving methods like Darboux and Bäcklund transformation, IST, Hirota bilinear, Lie groups, and time reversal, there are still nonlinear phenomena that are not completely understood. Rogue waves, for example, which have aroused scientists’ interest in plasmas, deep ocean, nonlinear optic, Bose–Einstein condensates, biophysics, superfluids, financial markets, and population dynamics, still cannot be predicted, and their generating mechanism is open to debate. Another example is pattern formation and the self-appearance of patterns for spatially extended systems. It is the aim of this Special Issue to gather some of the most debated and interesting topics from nonlinear science for which, in spite of the existence of highly developed mathematical tools of investigation, there are still fundamental open questions. Possible topics are new methods and applications in pattern-formation theory or the relationship between turbulence, solitary waves, breathers and rogue waves in oceanography, optical fibers, superfluids, BEC, and financial markets. Another topic is understanding the self-motion of compact systems like liquid drops, shells, bubbles, super-bubbles, anti-bubbles, vortex filaments, and their relationship to motile cells. The connection between the geometry of the boundaries and the structure of the solutions inside the bounded region is also an invited topic. Two- and four-wave mixing processes in nonlinear fluid dynamics and optics are also an important topic with modern applications in optical imaging, optical communications, real-time holography, and opto-electronic neural networks. Breathers as nonlinear excitations in DNA, self-generating of patterns scale-invariant networks, with applications in social and ecosystems, solitons in nonlinear lattices and stability of matter wave solitons in 2- and 3-dimensions, spontaneous formation of rotational patterns in fluids at different scale and regimes from Leidenfrost drops to oceans and galaxies are examples of topics hosted by this special issue.
Prof. Andrei Ludu
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.
Keywords
- Nonlinear dynamical processes
- Nonlinear fluid dynamics equations
- Nonlinear dispersion relations
- Phase transitions in nonlinear models for fluids
- Spontaneous pattern generation
- Solitons
- Breathers
- Darboux transformation
- Bäcklund transformation
- Bilinear Hirota
- Bose–Einstein condensate
- Rogue waves
- Inverse scattering theory
- Lie groups
- Time reversal
- Nonlinear models in social science
- Solitons in biology
- Liquid drops
- Liquid bubbles
- Liquid shells
- Fluid rotating patterns
- Scale-invariance in complex systems
- Nonlinear oscillators
- Nonlinear shape oscillations
- Nonlinear dispersion relations
- Nonlinearity in population dynamics.
