This book is an account of the underlying mathematical theory with emphasis on the unifying ideas and the main points that illuminate the behavior of waves. The mathematical ideas are liberally interspersed with discussion of specific cases and specific physical fields. The ideas are presented in general, and topics for application and motivation are chosen with a general reader in mind - for example, flood waves in rivers, waves in glaciers, traffic flow, sonic booms, blast waves and ocean waves from storms. The book is divided into two parts, the first on hyperbolic waves and the second on dispersive waves.
Introduction and General Outline.
· Waves and First Order Equations.
· Specific Problems.
· Burger's Equation.
· Hyperbolic Systems.
· Gas Dynamics.
· The Wave Equation.
· Shock Dynamics.
· The Propagation of Weak Shocks.
· Wave Hierarchies.
· Linear Dispersive Waves.
· Wave Patterns.
· Water Waves.
· Nonlinear Dispersion and the Variational Method.
· Group Velocities, Instability and Higher Order Dispersion.
· Applications of the Nonlinear Theory.
· Exact Solutions: Interacting Solitary Waves.
Researchers and Students in Applied Mathematics and Engineering.