Andrei Ludu

Nonlinear Waves and Solitons on Contours and Closed Surfaces (eBook, PDF)

• Format: PDF

Produktbeschreibung

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

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 466
• Erscheinungstermin: 9. September 2007
• Englisch
• ISBN-13: 9783540728733
• Artikelnr.: 37366253

Autorenporträt

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.

Inhaltsangabe

Introduction.- Topology and Algebra.- Vector Fields, Di erential Forms, and Derivatives.- The Importance of the Boundary.- Geometry of Curves.- Geometry of Surfaces.- Motion of Curves and Solitons.- Kinematics of Fluids.- Hydrodynamics.

Rezensionen

"The interested reader can find a sufficiently readable exposition of the basic ideas of this topic, taste the implementation of a wide range of analytical and numerical methods for obtaining new results ... and enjoy a comprehensive review of their applications. ... I would say that the third edition of the book Nonlinear Waves and Solitons on Contours and Closed Surfaces by Andrei Ludu is worth reading for everyone interested in the exciting theory of solitary waves ... ." (Vassil M. Vassilev, Journal of Geometry and Symmetry in Physics JGSP, Vol. 66, 2023)

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)