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Springer Series in Synergetics

Nonlinear Waves and Solitons on Contours and Closed Surfaces

Authors: Ludu, Andrei

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  • An introduction to nonlinear waves and soliton theory in the special environment of compact spaces
  • Emphasis is on the relevant notions from topology and differential geometry
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  • ISBN 978-3-540-72873-3
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About this book

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

About the authors

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.

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)


Table of contents (18 chapters)

Table of contents (18 chapters)

Buy this book

eBook $89.00
price for USA in USD
  • ISBN 978-3-540-72873-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $119.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Nonlinear Waves and Solitons on Contours and Closed Surfaces
Authors
Series Title
Springer Series in Synergetics
Copyright
2007
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-72873-3
DOI
10.1007/978-3-540-72873-3
Softcover ISBN
978-3-642-09196-4
Series ISSN
0172-7389
Edition Number
1
Number of Pages
XX, 466
Number of Illustrations
140 b/w illustrations
Topics

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