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Nonlinear waves are essential phenomena in scientific and
engineering disciplines. The features of nonlinear waves are
usually described by solutions to nonlinear partial differential
equations (NLPDEs). This book was prepared to familiarize students
with nonlinear waves and methods of solving NLPDEs, which will
enable them to expand their studies into related areas. The
selection of topics and the focus given to each provide essential
materials for a lecturer teaching a nonlinear wave course.Chapter 1
introduces 'mode' types in nonlinear systems as well as Bäcklund
transform, an indispensable technique to solve generic NLPDEs for
stationary solutions. Chapters 2 and 3 are devoted to the
derivation and solution characterization of three generic nonlinear
equations: nonlinear Schrödinger equation, Korteweg-de Vries (KdV)
equation, and Burgers equation. Chapter 4 is devoted to the inverse
scattering transform (IST), addressing the initial value problems
of a group of NLPDEs. In Chapter 5, derivations and proofs of the
IST formulas are presented. Steps for applying IST to solve NLPDEs
for solitary solutions are illustrated in Chapter 6.
Cold atmospheric plasma (CAP) generators have been actively
developed as a new device for medical treatment. The applications
of plasma treatment include 1) disinfection, sterilization, and
decontamination, which inactivates or kills bacteria, fungi,
viruses and spores; 2) bleeding control, which coagulates blood
swiftly; 3) wound healing, which shortens the healing period and
benefits the regeneration of the epithelization of tissue to avoid
scar formation; etc.Biomedical applications of CAPs are explored
via either in-vitro assays, or in-vivo tests using pigs as animal
models; tests include sterilization of oral pathogens and biofilm,
decontamination of biological warfare agent, blood clotting and
rapid control of active life-threatening hemorrhage, and
post-operative observation of wound healing after plasma treatment.
The conventional approaches in each application are first
introduced, then the advantages of plasma treatments are discussed
and demonstrated by the test results. The mechanisms of CAPs'
biocidal effect, blood clotting effect, and wound healing effect
are presented and discussed.
One essential feature of plasma media is supporting various plasma
waves and dictating electromagnetic wave propagation. This textbook
provides students with an understanding of plasma waves, which is
key to theoretical and experimental plasma research and
understanding the experimental results, and will enable them to
expand their studies into related areas.The first part of the text
provides the basis of plasma modes, including the formulations,
analyses and the physical characterizations. The second part
introduces techniques for the studies of wave propagation in
inhomogeneous plasma and of nonlinear mode-mode coupling in
turbulent plasma as well as in active plasma, applied to exemplify
the excitation of parametric instabilities in high-frequency (HF)
wave heated ionospheric plasma. The third part introduces nonlinear
plasma waves of periodic function forms and of solitary forms; a
potential application of the HF wave-ionosphere interaction for
setting up an ionospheric very-low-frequency transmitter for
underwater communications is introduced.This is also a useful
reference book for researchers in the areas of plasma physics and
engineering, and in geophysics.
Waves are essential phenomena in most scientific and engineering
disciplines, such as electromagnetism and optics, and different
mechanics including fluid, solid, structural, quantum, etc. They
appear in linear and nonlinear systems. Some can be observed
directly and others are not. The features of the waves are usually
described by solutions to either linear or nonlinear partial
differential equations, which are fundamental to the students and
researchers.Generic equations, describing wave and pulse
propagation in linear and nonlinear systems, are introduced and
analyzed as initial/boundary value problems. These systems cover
the general properties of non-dispersive and dispersive, uniform
and non-uniform, with/without dissipations. Methods of analyses are
introduced and illustrated with analytical solutions. Wave-wave and
wave-particle interactions ascribed to the nonlinearity of media
(such as plasma) are discussed in the final chapter.This
interdisciplinary textbook is essential reading for anyone in above
mentioned disciplines. It was prepared to provide students with an
understanding of waves and methods of solving wave propagation
problems. The presentation is self-contained and should be read
without difficulty by those who have adequate preparation in
classic mechanics. The selection of topics and the focus given to
each provide essential materials for a lecturer to cover the bases
in a linear/nonlinear wave course.
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