Dissipative Solitons: From Optics to Biology and Medicine

The dissipative soliton concept is a fundamental extension of the concept of solitons in conservative and integrable systems. It includes ideas from three major sources, namely standard soliton theory developed since the 1960s, nonlinear dynamics theory, and Prigogine's ideas of systems far from equilibrium. These three sources also correspond to the three component parts of this novel paradigm. This book explains the above principles in detail and gives the reader various examples from optics, biology and medicine. These include laser systems, optical transmission lines, cortical networks, models of muscle contraction, localized vegetation structures and waves in brain tissues.

Written for:
Scientists and graduate students

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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 "nonlinear modes" 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 "solitons are everywhere". 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 "Morning Glory" - a cloud wave hundreds of kilometers long - is also a dissipative soliton. During almost four decades of blossoming, soliton science produced brilliant results based on the "inverse scattering technique", 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 "integrable systems" does not fully allow us to describe real applications which do not exactly belong to the class of "integrable equations". Life is actually more complicated than the exceptional image of ideal solitons in an "integrable world".