This new edition has been thoroughly revised, expanded and contain some updates function of the novel results and shift of scientific interest in the topics. The book has a Foreword by Jerry L. Bona and Hongqiu Chen. The book 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.

Newly includes recent work on motion of solitons and of surfaces as well as 3D waves Provides the necessary mathematical framework for treating the manifolds considered with relevant notions from topology Applies the theory to many concrete examples appearing in the physical and related sciences

Autorentext
Dr. A. Ludu graduated in 1980 the MS Program in Theoretical Physics and Mathematics from University of Bucharest and he had received his Ph. D. in Physics in 1989 from the "H. Hulubei National Institute of Physics" in Bucharest-Magurele, Romania with a thesis on group transformations approach on hot and dense plasma. He worked for the national H Program on ultrahigh magnetic fields as a senior researcher in this Institute until 1985, after which he joined the Dept. Theoretical Physics of University of Bucharest as Associate Professor, until 1996. Between 1986 and 2001 he was postdoctoral researcher at Louisiana State University in Baton Rouge, and he joined Northwestern State University as Professor of Physics until 2011. At present he is Professor of Mathematics and Director of the Wave Lab in the Dept. of Mathematics at Embry-Riddle Aeronautical University in Daytona Beach. He published more than 80 peer reviewed paper in scientific journals and 4 books on the topics of solitons andnonlinear systems, applied differential geometry in physics, quantum groups, fluid dynamics, nuclear theory, biophysics, ultra-high energy density systems and wavelets. He was invited to work and give talks at prestigious centers of research including Los Alamos Natl. Lab, ICTP Trieste, Antwerp University, Université Libre de Bruxelles, US Navy Research Labs, Plymouth University, Trinity College, Niels Bohr Institute, Abo Akademi, Dalian University of Technology, etc. He was guest professor for more than ten years at J. Liebig University in Giessen and Goethe University in Frankfurt/Main, Germany. He was awarded the Mildred Hart Bailey Research Award and he is honorary member of several professional associations and science groups. In 1992 he predicted the existence of shape solitons orbiting on the surface of spheres (rotons). These predictions were continuously confirmed experimentally in systems like heavy nuclei collisions, flat electron drops, liquid drops and Leidenfrost drops and tori between 2007 and present. Dr. Ludu is married since 1980 to Maria, who is Professor of Mathematics at Embry-Riddle, and they have a daughter Delia, artist and graphic designer. He is VFR private pilot and practiced AMA enduro motorcycling, radio ham, and art photography.

Inhalt

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