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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
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.
Content Level »Research
Keywords »closed curves and surfaces - compact boundaries and surfaces - contour dynamics - introduction soliton theory - modeling of solitons - nonlinear waves introduced - physics of solitons - surface waves