Wave MotionWaves are a ubiquitous and important feature of the physical world, and, throughout history, it has been a major challenge to understand them. This introduction to the mathematics of wave phenomena is aimed at advanced undergraduate courses for mathematicians, physicists or engineers. Some more advanced material on both linear and nonlinear waves is also included, making the book suitable for beginning graduate courses. The authors assume some familiarity with partial differential equations, integral transforms and asymptotic expansions as well as with fluid mechanics, elasticity, and electromagnetism. The context and physics that underlie the mathematics is clearly explained at the beginning of each chapter. Worked examples and exercises are supplied throughout, with solutions available to teachers. |
Contents
Introduction | 1 |
Waves on a Stretched String | 17 |
4 | 29 |
Sound Waves | 36 |
3 | 42 |
5 | 50 |
7 | 64 |
Derivation of the Governing Equations | 74 |
Electromagnetic Waves | 173 |
Nonlinear Waves | 219 |
Nonlinear Water Waves | 269 |
Stokes Expansion | 280 |
Chemical and Electrochemical Waves | 308 |
Exercises | 349 |
Advanced Topics | 355 |
Diffraction and Scattering | 378 |
Other editions - View all
Common terms and phrases
acoustic asymptotic bound state eigenvalues boundary conditions capillary waves characteristics chemical components consider constant define density determine detonation wave differential equation diffraction diffusion dispersion eigenvalues electric field electromagnetic waves energy entropy example fluid flux Fourier free surface frequency function given gives group velocity H₁ hence homoclinic orbit incident wave initial conditions initial value problem integral interface inverse scattering transform K₁ KdV equation kinematic wave leading order linear magnetic field nonlinear Note obtain phase piston plane wave Pmax reflected wave reflectionless potential region satisfies shallow water shock wave shown in figure small amplitude solitary wave solitons string transform travelling wave solution tube variables vector water waves wave equation wave propagation wave speed waveguide wavelength wavenumber whilst write y₁ zero ди др ду дф дх