This 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.
Author(s): Andrei Ludu (auth.)
Series: Springer Series in Synergetics
Edition: 2
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2012
Language: English
Pages: 490
Tags: Nonlinear Dynamics;Differential Geometry;Mathematical Methods in Physics;Fluid- and Aerodynamics;Soft and Granular Matter, Complex Fluids and Microfluidics;Surface and Interface Science, Thin Films
Front Matter....Pages i-xviii
Front Matter....Pages 1-1
Introduction....Pages 3-8
Mathematical Prerequisites....Pages 9-22
The Importance of the Boundary....Pages 23-29
Vector Fields, Differential Forms, and Derivatives....Pages 31-77
Geometry of Curves....Pages 79-95
Geometry of Surfaces....Pages 97-130
Motion of Curves and Solitons....Pages 131-158
Theory of Motion of Surfaces....Pages 159-176
Front Matter....Pages 177-178
Kinematics of Hydrodynamics....Pages 179-221
Dynamics of Hydrodynamics....Pages 223-257
Nonlinear Surface Waves in One Dimension....Pages 259-288
Nonlinear Surface Waves in Two Dimensions....Pages 289-308
Nonlinear Surface Waves in Three Dimensions....Pages 309-372
Other Special Nonlinear Compact Systems....Pages 373-381
Front Matter....Pages 383-383
Filaments, Chains, and Solitons....Pages 385-410
Solitons on the Boundaries of Microscopic Systems....Pages 411-443
Nonlinear Contour Dynamics in Macroscopic Systems....Pages 445-466
Mathematical Annex....Pages 467-474
Back Matter....Pages 475-489
