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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.
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.
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)
"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)