Occurrence of nonlinear waves and instabilities in Nature

This book is concerned with the propagation of waves and instabilities both linear and nonlinear, but concentrating on the latter.

The main advances in this subject have quite naturally come from studies involving fluids and more recently plasmas. The latter primarily because of the possibility of ‘cheap, unlimited’ (and hopefully safe) power from thermonuclear reactions. Everyone is of course familiar with waves on water if only being aware of the many instances where they provide examples of natural beauty. It is not so obvious that very similar waves can exist in a plasma which, to a good approximation, is usually a very dilute assembly of ions and electrons. We shall see later in this chapter that this is indeed so and fluids and plasmas have much in common. However, plasmas also show a much wider range of phenomena basically because they are composed of two or more components and also can be made strongly anisotropic by the introduction of magnetic fields, something that is not possible for simple fluids. This richer variety of phenomena has also been a reason why plasmas have had more than their share of attention.

The above remarks notwithstanding, there are numerous media other than plasmas and fluids which can support waves and/or propagate instabilities. As we will see, some of these are more intriguing than others.