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)
Nonlinear Waves and Solitons on Contours and Closed Surfaces
von Andrei LuduThis volume is an introduction to nonlinear waves and soliton theory in the special environment of compact spaces such a closed curves and surfaces and other domain contours. It assumes familiarity with basic soliton theory and nonlinear dynamical systems.
The first part of the book introduces the mathematical concept required for treating the manifolds considered, providing relevant notions from topology and differential geometry. An introduction to the theory of motion of curves and surfaces - as part of the emerging field of contour dynamics - is given.
The second and third parts discuss the modeling of various physical solitons on compact systems, such as filaments, loops and drops made of almost incompressible materials thereby intersecting with a large number of physical disciplines from hydrodynamics to compact object astrophysics.
This book is intended for graduate students and researchers in mathematics, physics and engineering.
This new edition has been thoroughly revised, expanded and updated.
