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| Introduction | p. 1 |
| Linear Waves | p. 5 |
| Basic Ideas | p. 7 |
| Exercises | p. 15 |
| Waves on a Stretched String | p. 17 |
| Derivation of the Governing Equation | p. 17 |
| Standing Waves on Strings of Finite Length | p. 20 |
| D'Alembert's Solution for Strings of Infinite Length | p. 26 |
| Reflection and Transmission of Waves by Discontinuities in Density | p. 29 |
| A Single Discontinuity | p. 29 |
| Two Discontinuities: Impedance Matching | p. 31 |
| Exercises | p. 33 |
| Sound Waves | p. 36 |
| Derivation of the Governing Equation | p. 36 |
| Plane Waves | p. 40 |
| Acoustic Energy Transmission | p. 42 |
| Plane Waves In Tubes | p. 45 |
| Acoustic Waveguides | p. 50 |
| Reflection of a Plane Acoustic Wave by a Rigid Wall | p. 50 |
| A Planar Waveguide | p. 51 |
| A Circular Waveguide | p. 53 |
| Acoustic Sources | p. 57 |
| The Acoustic Source | p. 58 |
| Energy Radiated by Sources and Plane Waves | p. 62 |
| Radiation from Sources in a Plane Wall | p. 64 |
| Exercises | p. 70 |
| Linear Water Waves | p. 74 |
| Derivation of the Governing Equations | p. 74 |
| Linear Gravity Waves | p. 78 |
| Progressive Gravity Waves | p. 78 |
| Standing Gravity Waves | p. 85 |
| The Wavemaker | p. 87 |
| The Extraction of Energy from Water Waves | p. 91 |
| The Effect of Surface Tension: Capillary--Gravity Waves | p. 94 |
| Edge Waves | p. 97 |
| Ship Waves | p. 99 |
| The Solution of Initial Value Problems | p. 104 |
| Shallow Water Waves: Linear Theory | p. 109 |
| The Reflection of Sea Swell by a Step | p. 112 |
| Wave Amplification at a Gently Sloping Beach | p. 114 |
| Wave Refraction | p. 117 |
| The Kinematics of Slowly Varying Waves | p. 118 |
| Wave Refraction at a Gently Sloping Beach | p. 121 |
| The Effect of Viscosity | p. 123 |
| Exercises | p. 124 |
| Waves in Elastic Solids | p. 130 |
| Derivation of the Governing Equation | p. 130 |
| Waves in an Infinite Elastic Body | p. 132 |
| One-Dimensional Dilatation Waves | p. 133 |
| One-Dimensional Rotational Waves | p. 134 |
| Plane Waves with General Orientation | p. 134 |
| Two-Dimensional Waves in Semi-infinite Elastic Bodies | p. 135 |
| Normally Loaded Surface | p. 135 |
| Stress-Free Surface | p. 137 |
| Waves in Finite Elastic Bodies | p. 143 |
| Flexural Waves in Plates | p. 144 |
| Waves in Elastic Rods | p. 148 |
| Torsional Waves | p. 150 |
| Longitudinal Waves | p. 155 |
| The Excitation and Propagation of Elastic Wavefronts | p. 156 |
| Wavefronts Caused by an Internal Line Force in an Unbounded Elastic Body | p. 157 |
| Wavefronts Caused by a Point Force on the Free Surface of a Semi-infinite Elastic Body | p. 161 |
| Exercises | p. 168 |
| Electromagnetic Waves | p. 173 |
| Electric and Magnetic Forces and Fields | p. 173 |
| Electrostatics: Gauss's Law | p. 177 |
| Magnetostatics: Ampere's Law and the Displacement Current | p. 179 |
| Electromagnetic Induction: Farady's Law | p. 180 |
| Plane Electromagnetic Waves | p. 182 |
| Conductors and Insulators | p. 186 |
| Reflection and Transmission at Interfaces | p. 189 |
| Boundary Conditions at Interfaces | p. 189 |
| Reflection by a Perfect Conductor | p. 191 |
| Reflection and Refraction by Insulators | p. 194 |
| Waveguides | p. 199 |
| Metal Waveguides | p. 199 |
| Weakly Guiding Optical Fibres | p. 202 |
| Radiation | p. 208 |
| Scalar and Vector Potentials | p. 208 |
| The Electric Dipole | p. 210 |
| The Far Field of a Localised Current Distribution | p. 212 |
| The Centre Fed Linear Antenna | p. 213 |
| Exercises | p. 216 |
| Nonlinear Waves | p. 219 |
| The Formation and Propagation of Shock Waves | p. 221 |
| Traffic Waves | p. 221 |
| Derivation of the Governing Equation | p. 221 |
| Small Amplitude Disturbances of a Uniform State | p. 224 |
| The Nonlinear Initial Value Problem | p. 226 |
| The Speed of the Shock | p. 236 |
| Compressible Gas Dynamics | p. 239 |
| Some Essential Thermodynamics | p. 239 |
| Equations of Motion | p. 243 |
| Construction of the Characteristic Curves | p. 245 |
| The Rankine--Hugoniot Relations | p. 249 |
| Detonations | p. 256 |
| Exercises | p. 266 |
| Nonlinear Water Waves | p. 269 |
| Nonlinear Shallow Water Waves | p. 269 |
| The Dam Break Problem | p. 270 |
| A Shallow Water Bore | p. 275 |
| The Effect of Nonlinearity on Deep Water Gravity Waves: Stokes' Expansion | p. 280 |
| The Korteweg-de Vries Equation for Shallow Water Waves: the Interaction of Nonlinear Steepening and Linear Dispersion | p. 285 |
| Derivation of the Korteweg-de Vries Equation | p. 287 |
| Travelling Wave Solutions of the KdV Equation | p. 290 |
| Nonlinear Capillary Waves | p. 298 |
| Exercises | p. 306 |
| Chemical and Electrochemical Waves | p. 308 |
| The Law of Mass Action | p. 310 |
| Molecular Diffusion | p. 314 |
| Reaction-Diffusion Systems | p. 315 |
| Autocatalytic Chemical Waves with Unequal Diffusion Coefficients* | p. 326 |
| Existence of Travelling Wave Solutions | p. 327 |
| Asymptotic Solution for [delta] [[ 1 | p. 330 |
| The Transmission of Nerve Impulses: the Fitzhugh-Nagumo Equations | p. 334 |
| The Fitzhugh-Nagumo Model | p. 339 |
| The Existence of a Threshold | p. 342 |
| Travelling Waves | p. 343 |
| Exercises | p. 349 |
| Advanced Topics | p. 355 |
| Burgers' Equation: Competition between Wave Steepening and Wave Spreading | p. 357 |
| Burgers' Equation for Traffic Flow | p. 357 |
| The Effect of Dissipation on Weak Shock Waves in an Ideal Gas | p. 362 |
| Simple Solutions of Burgers' Equation | p. 369 |
| Travelling Waves | p. 369 |
| Asymptotic Solutions for v [[ 1 | p. 370 |
| Exercises | p. 375 |
| Diffraction and Scattering | p. 378 |
| Diffraction of Acoustic Waves by a Semi-infinite Barrier | p. 379 |
| Preliminary Estimates of the Potential | p. 380 |
| Pre-transform Considerations | p. 383 |
| The Fourier Transform Solution | p. 385 |
| The Diffraction of Waves by an Aperture | p. 391 |
| Scalar Diffraction: Acoustic Waves | p. 391 |
| Vector Diffraction: Electromagnetic Waves | p. 394 |
| Scattering of Linear, Deep Water Waves by a Surface Piercing Cylinder | p. 399 |
| Exercises | p. 403 |
| Solitons and the Inverse Scattering Transform | p. 405 |
| The Korteweg-de Vries Equation | p. 406 |
| The Scattering Problem | p. 406 |
| The Inverse Scattering Problem | p. 410 |
| Scattering Data for KdV Potentials | p. 416 |
| Examples: Solutions of the KdV Equation | p. 418 |
| The Nonlinear Schrodinger Equation | p. 424 |
| Derivation of the Nonlinear Schrodinger Equation for Plane Electromagnetic Waves | p. 424 |
| Solitary Wave Solutions of the Nonlinear Schrodinger Equation | p. 431 |
| The Inverse Scattering Transform for the Nonlinear Schrodinger Equation | p. 435 |
| Exercises | p. 448 |
| Useful Mathematical Formulas and Physical Data | p. 451 |
| Cartesian Coordinates | p. 451 |
| Cylindrical Polar Coordinates | p. 451 |
| Spherical Polar Coordinates | p. 452 |
| Some Vector Calculus Identities and Useful Results for Smooth Vector Fields | p. 453 |
| Physical constants | p. 454 |
| Bibliography | p. 455 |
| Index | p. 459 |
| Table of Contents provided by Syndetics. All Rights Reserved. |
ISBN: 9780521634502
ISBN-10: 0521634504
Series: Cambridge Texts in Applied Mathematics, 24
Published: 2nd April 2001
Format: Paperback
Language: English
Number of Pages: 476
Audience: Professional and Scholarly
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.86 x 15.24 x 2.69
Weight (kg): 0.69
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