The aim of publishing this book is the further development of the concept of dissipative solitons, which has been in the air for at least the last decade and a half. Since the development of classical soliton theory in the 1960s, the theory of these ânonlinear modesâ of integrable systems outgrew its initial ideas. The purely mathematical concept, as it appeared in the work of Zabusky and Kruskal in 1965, required experimental veri cation, and this was successfully carried out in liquids, optical bers, and some other exotic media. Scientists came to the conclusion that âsolitons are everywhereâ. Indeed, the notion of solitons gave a powerful boost to the multibillion industry of telecommunications. The idea of solitons underlies our understanding of tidal bores, cyclones and massive ocean waves like tsunamis. There is no doubt that the magni cent phenomenon known as âMorning Gloryâ â a cloud wave hundreds of kilometers long â is also a dissipative soliton. During almost four decades of blossoming, soliton science produced brilliant results based on the âinverse scattering techniqueâ, which allowed for construction of soliton solutions for a variety of integrable systems describing physics of water waves, light propagation, etc. At the same time, experimental scientists realized that the framework of a few particular âintegrable systemsâ does not fully allow us to describe real applications which do not exactly belong to the class of âintegrable equationsâ. Life is actually more complicated than the exceptional image of ideal solitons in an âintegrable worldâ.
