Nonlinear Waves

The outcome of a conference held in East Carolina University in June 1982, this book provides an account of developments in the theory and application of nonlinear waves in both fluids and plasmas.

This book addresses the peculiarities of nonlinear wave propagation in waveguides and explains how the stratification depends on the waveguide and confinement. An example of this is an optical fibre that does not allow light to pass through a density jump. The book also discusses propagation in the nonlinear regime, which is characterized by a specific waveform and amplitude, to demonstrate so-called solitonic behaviour. In this case, a wave may be strongly localized, and propagates with a weak change in shape.

This book addresses the fascinating phenomena associated with nonlinear waves and spatio-temporal patterns. These appear almost everywhere in nature from sand bed forms to brain patterns, and yet their understanding still presents fundamental scientific challenges.

This book unifies the dynamical systems and functional analysis approaches to the linear and nonlinear stability of waves. It synthesizes fundamental ideas of the past 20+ years of research, carefully balancing theory and application. The book isolates and methodically develops key ideas by working through illustrative examples that are subsequently synthesized into general principles.