Authors:
- Fully revised and updated 2nd edition transparently introduces the theory of nonlinear waves and solitons in the special environment of compact spaces
- Provides the necessary mathematical framework for treating the manifolds considered with relevant notions from topology and differential geometry
- Applies the theory to many concrete examples appearing in the physical and related sciences
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Series in Synergetics (SSSYN)
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Table of contents (18 chapters)
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Front Matter
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Solitons and Nonlinear Waves on Closed Curves and Surfaces
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Front Matter
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Physical Nonlinear Systems at Different Scales
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Front Matter
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About this book
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.
Reviews
From the reviews of the second edition:
“This book is devoted to the detailed exposition of the present state of research in the field of nonlinear dynamics of boundaries of physical systems which in the two-dimensional case reduces to the so-called contour dynamics. … The text is intended to be an introduction to the physics and mathematics of solitons on compact systems … . In general, this book can serve as a source of information for students and researchers in nonlinear physics on nonlinear dynamics of compact systems.” (Anatoly M. Kamchatnov, Mathematical Reviews, September, 2013)
“This book is an update of the first edition … and deals with models of nonlinear media filling closed (compact) curves and surfaces. The main subject is a systematic construction and study of solitons states in such systems. … the book may be used as a basis for a graduate course on the theory of nonlinear waves and solitons.” (Boris A. Malomed, Zentralblatt MATH, Vol. 1253, 2013)
Authors and Affiliations
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, Department of Mathematics, Embry-Riddle Aeronautical University, Daytona Beach, USA
Andrei Ludu
Bibliographic Information
Book Title: Nonlinear Waves and Solitons on Contours and Closed Surfaces
Authors: Andrei Ludu
Series Title: Springer Series in Synergetics
DOI: https://doi.org/10.1007/978-3-642-22895-7
Publisher: Springer Berlin, Heidelberg
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2012
Softcover ISBN: 978-3-642-44051-9Published: 22 February 2014
eBook ISBN: 978-3-642-22895-7Published: 14 January 2012
Series ISSN: 0172-7389
Series E-ISSN: 2198-333X
Edition Number: 2
Number of Pages: XVIII, 490
Topics: Applications of Nonlinear Dynamics and Chaos Theory, Differential Geometry, Mathematical Methods in Physics, Fluid- and Aerodynamics, Soft and Granular Matter, Complex Fluids and Microfluidics, Surface and Interface Science, Thin Films