Linear and Nonlinear Waves

Gerald Beresford Whitham was a British-born American applied mathematician and the Charles Lee Powell Professor of Applied Mathematics of Applied & Computational Mathematics at the California Institute of Technology.

Introduction and General Outline.

HYPERBOLIC WAVES.

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.

DISPERSIVE WAVES.

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.

References.

Index.