Nonlinear Waves in Bounded Media

The Mathematics of Resonance

This unique book aims to treat a class of nonlinear waves that are reflected from the boundaries of media of finite extent. It involves both standing (unforced) waves and resonant oscillations due to external periodic forcing. The waves are both hyperbolic and dispersive. To achieve this aim, the book develops the necessary understanding of linear waves and the mathematical techniques of nonlinear waves before dealing with nonlinear waves in bounded media. The examples used come mainly from gas dynamics, water waves and viscoelastic waves.

Contents:

• Introduction
• Physical Examples: Basic Equations
• Classical Linear Solutions
• Linear Physical Examples
• Linear Waves in Stratified Media
• Kinematic and Simple Waves
• Nonlinear Geometric Acoustics
• Bounded Media
• Nonlinear Resonance: Shocked Solutions
• Finite Rate Oscillations
• The Evolution of Resonant Oscillations
• Shaped and Stratified Resonators
• Resonant Sloshing in a Shallow Tank

Readership: Advanced undergraduate and graduate students, researchers and practitioners in the field of acoustics, fluid mechanics and applied physics.
Key Features:

• The only book dealing with nonlinear waves in bounded media
• Highlights the introduction and analysis of solutions of a nonlinear difference equation — the standard mapping — that connects shocked resonance to chaos
• Introduces many concepts and publishes extensively in the literature of nonlinear waves and nonlinear resonance