Nonlinear Waves 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 : Imprint: Springer, 2012.
• Edition: 2nd ed. 2012.
• Series: Springer Series in Synergetics,
• Subjects: Physics.; Differential geometry.; Fluids.; Amorphous substances.; Complex fluids.; Surfaces (Physics).; Interfaces (Physical sciences).; Thin films.; Statistical physics.; Nonlinear Dynamics.; Differential Geometry.; Mathematical Methods in Physics.; Fluid- and Aerodynamics.; Soft and Granular Matter, Complex Fluids and Microfluidics.; Surface and Interface Science, Thin Films.

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 m...

Table of Contents:

• Introduction
• 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
• 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
• Filaments, Chains and Solitons
• Solitons on the Boundaries of Microscopic Systems
• Nonlinear Contour Dynamics in Macroscopic Systems
• Mathematical Annex
• References
• Index.