Description 
1 online resource (xviii, 464 pages) : illustrations 
Series 
Springer complexity 

Springer series in synergetics, 01727389 

Springer complexity


Springer series in synergetics (Unnumbered)

Contents 
Mathematical Prerequisites  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  Solitons and Nonlinear Waves on Closed Curves and 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  Physical Nonlinear Systems at Different Scales  Filaments, Chains, and Solitons  Solitons on the Boundaries of Microscopic Systems  Nonlinear Contour Dynamics in Macroscopic Systems  Mathematical Annex 
Summary 
The present 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. Emphasis on the 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. Nonlinear Waves and Solitons on Contours and Closed Surfaces provides graduate students and researchers in mathematics, physics and engineering with a ready tutorial and reference 
Bibliography 
Includes bibliographical references (pages 453460) and index 
Subject 
Nonlinear waves  Mathematics


Solitons  Mathematics


Compact spaces.


SCIENCE  Waves & Wave Mechanics.


Compact spaces.


Nonlinear waves  Mathematics.


Solitons  Mathematics.


Physique.


Compact spaces.


Nonlinear waves  Mathematics.


Solitons  Mathematics.

Form 
Electronic book

ISBN 
9783540728733 

3540728732 

9783540728726 

3540728724 

9786611066703 

6611066705 
