The most readable survey of the theoretical core of current knowledge available. The author gives a concise account of the classical theory necessary to an understanding of the subject and considers how this theory has been extended to solids.

Self-contained coverage of topics ranging from elementary theory of waves and vibrations in strings to three-dimensional theory of waves in thick plates. Over 100 problems.

This book is based on an undergraduate course taught at the IAS/Park City Mathematics Institute (Utah) on linear and nonlinear waves. The first part of the text overviews the concept of a wave, describes one-dimensional waves using functions of two variables, provides an introduction to partial differential equations, and discusses computer-aided visualization techniques. The second part of the book discusses traveling waves, leading to a description of solitary waves and soliton solutions of the Klein-Gordon and Korteweg-deVries equations. The wave equation is derived to model the small vibrations of a taut string, and solutions are constructed via d'Alembert's formula and Fourier series.The last part of the book discusses waves arising from conservation laws. After deriving and discussing the scalar conservation law, its solution is described using the method of characteristics, leading to the formation of shock and rarefaction waves. Applications of these concepts are then given for models of traffic flow. The intent of this book is to create a text suitable for independent study by undergraduate students in mathematics, engineering, and science. The content of the book is meant to be self-contained, requiring no special reference material. Access to computer software such as MathematicaR, MATLABR, or MapleR is recommended, but not necessary. Scripts for MATLAB applications will be available via the Web. Exercises are given within the text to allow further practice with selected topics.

?Density Waves in Solids is written for graduate students and scientists interested in solid-state sciences. It discusses the theoretical and experimental state of affairs of two novel types of broken symmetry ground states of metals, charge, and spin density waves. These states arise as the consequence of electron-phonon and electron-electron interactions in low-dimensional metals.Some fundamental aspects of the one-dimensional electron gas, and of the materials with anisotropic properties, are discussed first. This is followed by the mean field theory of the phases transitions?discussed using second quantized formalism?together with the various experimental observations on the transition and on the ground states. Fluctuation effects and the collective excitations are reviewed next, using the Ginzburg-Landau formalism, followed by the review of the interaction of these states with the underlying lattice and with impurities. The final chapters are devoted to the response of the ground states to external perturbations.

Magnetic materials can support propagating waves of magnetization; since these are oscillations in the magnetostatic properties of the material, they are called magnetostatic waves (sometimes "magnons" or "magnetic polarons"). Under the proper circumstances these waves can exhibit, for example, either dispersive or nondispersive, isotropic or anisotropic propagation, nonreciprocity, frequency-selective nonlinearities, soliton propagation, and chaotic behavior. This rich variety of behavior has led to a number of proposed applications in microwave and optical signal processing. This textbook begins by discussing the basic physics of magnetism in magnetic insulators and the propagation of electromagnetic waves in anisotropic dispersive media. It then treats magnetostatic modes, describing how the modes are excited, how they propagate, and how they interact with light. There are problems at the end of each chapter; many of these serve to expand or explain the material in the text. To enhance the book's usefulness as a reference, the answers are given for many of the problems. The bibliographies for each chapter give an entry to the research literature. Magnetostatic Waves will thus serve not only as an introduction to an active area of research, but also as a handy reference for workers in the field.

Authored by the internationally renowned José M. Carcione, Wave Fields in Real Media: Wave Propagation in Anisotropic, Anelastic, Porous and Electromagnetic Media examines the differences between an ideal and a real description of wave propagation, starting with the introduction of relevant stress-strain relations. The combination of this relation and the equations of momentum conservation lead to the equation of motion. The differential formulation is written in terms of memory variables, and Biot's theory is used to describe wave propagation in porous media. For each rheology, a plane-wave analysis is performed in order to understand the physics of wave propagation. This book contains a review of the main direct numerical methods for solving the equation of motion in the time and space domains. The emphasis is on geophysical applications for seismic exploration, but researchers in the fields of earthquake seismology, rock acoustics, and material science - including many branches of acoustics of fluids and solids - may also find this text useful. New to this edition: This new edition presents the fundamentals of wave propagation in Anisotropic, Anelastic, Porous Media while also incorporating the latest research from the past 7 years, including that of the author. The author presents all the equations and concepts necessary to understand the physics of wave propagation. These equations form the basis for modeling and inversion of seismic and electromagnetic data. Additionally, demonstrations are given, so the book can be used to teach post-graduate courses. Addition of new and revised content is approximately 30%. Examines the fundamentals of wave propagation in anisotropic, anelastic and porous media Presents all equations and concepts necessary to understand the physics of wave propagation, with examples Emphasizes geophysics, particularly, seismic exploration for hydrocarbon reservoirs, which is essential for exploration and production of oil