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Book Cover
Author Ludu, Andrei

Title Nonlinear waves and solitons on contours and closed surfaces / Andrei Ludu
Edition 2nd ed
Published Berlin ; New York : Springer, ©2012


Description 1 online resource (xviii, 489 pages) : illustrations
Series Springer series in synergetics, 0172-7389
Springer complexity
Springer series in synergetics (Unnumbered)
Springer complexity
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
Summary Annotation 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
Analysis Physics
Global differential geometry
Mathematical physics
Nonlinear Dynamics
Differential Geometry
Mathematical Methods in Physics
Fluid- and Aerodynamics
Soft and Granular Matter, Complex Fluids and Microfluidics
Surface and Interface Science, Thin Films
Bibliography Includes bibliographical references and index
Subject Nonlinear waves -- Mathematics
Solitons -- Mathematics
Compact spaces.
SCIENCE -- Waves & Wave Mechanics.
Compact spaces.
Nonlinear waves -- Mathematics.
Solitons -- Mathematics.
Form Electronic book
ISBN 9783642228957