Nonlinear Waves and Solitons on Contours and Closed Surfaces
Series: Springer Series in Synergetics;
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Product details:
- Publisher Springer
- Date of Publication 19 September 2007
- Number of Volumes Book
- ISBN 9783540728726
- Binding Hardback
- No. of pages466 pages
- Size 235x155 mm
- Language English
- Illustrations 140 Illustrations, black & white; 1 Tables, black & white 0
Categories
Short description:
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
Long description:
The present volume is an introduction to nonlinear waves and soliton theory in the special environment of compact spaces such as closed curves and surfaces and other domain contours.
The first part of the book introduces the mathematical concept required for treating the manifolds considered. An introduction to the theory of motion of curves and surfaces is given. The second and third parts discuss the modeling of various physical solitons on compact systems.
From the reviews:
"The author succeeds in writing a monograph which introduces the physics of solitons on compact systems to readers who may not have any such prior knowledge. … The text is suitable for a graduate course on special topics or it can be used by readers with various backgrounds and interests who simply want to understand the connections between geometry and the phenomena of nonlinear waves." (Alina Stancu, Zentralblatt MATH, Vol. 1167, 2009)
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.
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