Everything the Power of the World does is done in a circle. The sky is round and I have heard that the earth is round like a ball and so are all the stars. The wind, in its greatest power, whirls. Birds make their nests in circles, for theirs is the same religion as ours. The sun comes forth and goes down again in a circle. The moon does the same and both are round. Even the seasons form a great circle in their changing and always come back again to where they were. The life of a man is a circle from childhood to childhood. And so it is everything where power moves. Black Elk (1863-1950) Nonlinearity is a captivating manifestation of the observable Universe, whose importance has increased over the decades, and has found more and more ?elds of application ranging from elementary particles, nuclear physics, biology, wave dynamics at any scale, ?uids, plasmas to astrophysics. The central character of this 172-year-old story is the soliton. Namely, a localized pulse traveling withoutspreading and having particle-like properties plus an in?nite number of conservation laws associated to its dynamics. In general, solitons arise as exact solutions of approximative models. There are di?- ent explanation, at di?erent levels, for the existence of solitons. From the experimentalist point of view, solitons can be created if the propagation c- ?gurationislongenough,narrowenough(likelongandshallowchannels,?ber optics, electric lines, etc.
From the reviews of the second edition:
"This book is devoted to the detailed exposition of the present state of research in the field of nonlinear dynamics of boundaries of physical systems which in the two-dimensional case reduces to the so-called contour dynamics. ... The text is intended to be an introduction to the physics and mathematics of solitons on compact systems ... . In general, this book can serve as a source of information for students and researchers in nonlinear physics on nonlinear dynamics of compact systems." (Anatoly M. Kamchatnov, Mathematical Reviews, September, 2013)
"This book is an update of the first edition ... and deals with models of nonlinear media filling closed (compact) curves and surfaces. The main subject is a systematic construction and study of solitons states in such systems. ... the book may be used as a basis for a graduate course on the theory of nonlinear waves and solitons." (Boris A. Malomed, Zentralblatt MATH, Vol. 1253, 2013)
"This book is devoted to the detailed exposition of the present state of research in the field of nonlinear dynamics of boundaries of physical systems which in the two-dimensional case reduces to the so-called contour dynamics. ... The text is intended to be an introduction to the physics and mathematics of solitons on compact systems ... . In general, this book can serve as a source of information for students and researchers in nonlinear physics on nonlinear dynamics of compact systems." (Anatoly M. Kamchatnov, Mathematical Reviews, September, 2013)
"This book is an update of the first edition ... and deals with models of nonlinear media filling closed (compact) curves and surfaces. The main subject is a systematic construction and study of solitons states in such systems. ... the book may be used as a basis for a graduate course on the theory of nonlinear waves and solitons." (Boris A. Malomed, Zentralblatt MATH, Vol. 1253, 2013)