Overview

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.

Full Product Details

Author:   Andrei Ludu
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Dimensions:   Width: 15.50cm , Height: 3.20cm , Length: 23.50cm
Weight:   0.839kg
ISBN:  

9783540728726

ISBN 10:   3540728724
Pages:   486
Publication Date:   19 September 2007
Audience:   College/higher education ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of stock  
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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: 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)

Author Information

Nonlinear and solitary waves are historically related to quasi one-dimensional systems where the spatial extent in one direction is much bigger than in the other direction, such as channels and fibres. The present book treats the case of more compact systems and their nonlinear ascillations, which have only recently come into forms. Such systems include liquid drop models, Bose-Einstein condensates and even living cells. A general formalism is developed, based on the differential geometry of curved manifolds, and various applications are considered in the physical sciences and beyond.

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