Table of Contents

Introduction.- Mathematical Prerequisites.- The Importance of the Boundary.- Vector Fields, Differential Forms, and Derivatives.- Geometry of Curves.- Motion of Curves and Solitons.- Geometry of Surfaces.- Theory of Motion of Surfaces.- Kinematics of Hydrodynamics.- Dynamics of Hydrodynamics.- Nonlinear Surface Waves in One-Dimension.- Nonlinear Surface Waves in Two-Dimensions.- Nonlinear Surface Waves in Three-Dimensions.- Other Special Nonlinear Compact Systems.- Filaments, Chains and Solitons.- Solitons on the Boundaries of Microscopic Systems.- Nonlinear Contour Dynamics in Macroscopic Systems.- Mathematical Annex.- References.- Index.

Reviews

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)