Nonlinear Waves and Applications
A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C2: Dynamical Systems".
Deadline for manuscript submissions: closed (31 May 2020) | Viewed by 2572
Special Issue Editor
Interests: nonlinear waves; applied dynamical systems; nonlinear Schrödinger equation
Special Issues, Collections and Topics in MDPI journals
Special Issue Information
Dear Colleagues,
This Special Issue, “Nonlinear Waves and Applications”, will be open for the publication of high-quality mathematical papers in the area of nonlinear waves (integrable and non-integrable systems, discrete and continuous equations). Nonlinear dispersive wave equations provide excellent examples of infinite dimensional dynamical systems which possess diverse and fascinating solutions, including solitary waves, pattern formation, singularity formation, localized time-periodic structures, dispersive turbulence, and spatiotemporal chaos. The evolution equations (discrete and continuous systems) can be used to illustrate many striking features of nonlinear waves, each of which has been understood by a combination of methods from scientific computations and from the theory of PDEs, applied analysis, and dynamical systems. These features include solitary waves and solitons, periodic waves and quasi-periodic wavetrains, long-time asymptotics, finite time blow-up, instabilities and unstable manifolds, and spatiotemporal chaos.
One of the more exciting areas in applied mathematics is the study of the dynamics associated with the propagation of information. Phenomena of interest include the transmission of impulses in nerve fibers, the transmission of light down an optical fiber, and phase transitions in materials. The nature of the system dictates that the relevant and important effects occur along one axial direction. The models formulated in these areas exhibit many other effects, but it is these nonlinear waves that are the raison-dŠetre of the models. The demands on the mathematician for techniques to analyze these models may best be served by developing methods tailored to determining the local behavior of solutions near these structures.
Papers involving all those abovementioned topics are welcome. Moreover, this Special Issue gives an opportunity to researchers and practitioners to communicate their ideas.
Prof. Dr. Vassilis M Rothos
Guest Editor
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