Wave MotionCambridge University Press, 22 հնվ, 2001 թ. Waves are a ubiquitous and important feature of the physical world, and throughout history it has been a major challenge to understand them. They can propagate on the surfaces of solids and of fluids; chemical waves control the beating of your heart; traffic jams move in waves down lanes crowded with vehicles. This introduction to the mathematics of wave phenomena is aimed at advanced undergraduate courses on waves for mathematicians, physicists or engineers. Some more advanced material on both linear and nonlinear waves is also included, thus 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 an acquaintance 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. |
Բովանդակություն
| 1 | |
| 5 | |
Nonlinear Waves | 219 |
Advanced Topics | 351 |
Appendix 1 Useful Mathematical Formulas and Physical Data
| 447 |
Bibliography | 451 |
| 455 | |
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acoustic asymptotic bound state eigenvalues boundary condition capillary waves characteristics chemical components consider constant define density determine differential equation diffraction dispersion relation displacement eigenvalues elastic electric field electromagnetic waves energy example finite fluid flux free surface frequency function given gives governing equations gravity waves group velocity hence homoclinic orbit incident wave initial conditions initial value problem integral interface KdV equation kinematic wave leading order linear linearised magnetic field nonlinear Note obtain one-dimensional phase piston plane wave reflected wave reflectionless potential region satisfies shallow water shock wave shown in figure small amplitude ſº solitary wave solitons string travelling wave solution tube variables vector water waves wave crests wave equation wave propagation wave speed waveguide wavelength wavenumber whilst write x-direction zero