Abstract

Solitons, i.e. solitary localized waves with particle-like behaviour, and multi-solitons occur virtually everywhere. There is a good reason for that in that there is a solid, albeit somewhat heuristic argument which says that for wave-like phenomena the 'soliton approximation' is the next one after the linear one. It is also not too difficult via some searching in the voluminous literature - many hundreds of papers on solitons each year - to write down a long list of equations which admit soliton solutions and which model phenomena ranging over all the physical, biological, chemical and geological sciences as well as engineering. Yet, when lecturing on (mathematical) aspects of solitons I have found it not so easy to go beyond listing these equations. Largely because of lack of a book like this, which discusses where and how solitons arise, how they behave, whether or not they are stable and in what sense, which discusses approximate solitons and solitons in multidimensional spaces (which in a first simple natural formulation cannot exist), which discusses soliton (computer) experiments; all this for a wide range of phenomena especially in connection with solid state physics. There is a great deal of analytic material as well as there is especially a considerable collection of challenges for theoretical understanding. A great deal of the material covered in this book has not appeared in the monographic literature before. The phenomenology of solitons is very rich indeed.