Nonlinear Waves and Solitons on Contours and Closed Surfaces

Download or read book Nonlinear Waves and Solitons on Contours and Closed Surfaces written by Andrei Ludu and published by Springer Science & Business Media. This book was released on 2012-01-15 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.