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.