NonlinearWaves and Solitons on Contours and Closed Surfaces

• Main Author: Ludu, Andrei (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2007.
• Series: Springer Series in Synergetics,
• Subjects: Physics.; Dynamics.; Ergodic theory.; Differential geometry.; Mechanics.; Fluids.; Statistical physics.; Dynamical systems.; Statistical Physics, Dynamical Systems and Complexity.; Dynamical Systems and Ergodic Theory.; Differential Geometry.; Mathematical Methods in Physics.; Fluid- and Aerodynamics.

The present 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 introduce...

Table of Contents:

• Mathematical Prerequisites
• 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
• Solitons and Nonlinear Waves on Closed Curves and 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
• Physical Nonlinear Systems at Different Scales
• Filaments, Chains, and Solitons
• Solitons on the Boundaries of Microscopic Systems
• Nonlinear Contour Dynamics in Macroscopic Systems
• Mathematical Annex.