When this book was first published in 1990, it became more popular than we expected. A book club chose it as its Book of the Month. It was reprinted in 1992. Eight years have now gone by and we feel it is time for a proper revision. New results and references have been added. On the other hand, some chapters remain largely as they were, since we feel that the presentation of the basic ideas to be found there remains valid. Chapter 11 (Chapter 10 in the first edition) on chaotic phenomena is an example of this.

The only criticism anyone made to our faces was that we leaned too heavily on plasma physics and hydrodynamics for examples, whereas most phenomena and methods we consider have wider applications. These include optics, biology, solid state physics and other fields. This shortcoming has now been rectified to a certain extent. Also, a new chapter on soliton metamorphosis, including some colour plates, has been added (Chapter 10).

However, much of the text has been left as it was. Thus ‘recent’ should be read as recent in 1990. Some printing errors have been corrected. Once again, Dr Simon Capelin of the Cambridge University Press has been patient and helpful. Ms Lenkowska-Czerwihska spent a large portion of her time in Warwick helping us organize our material.