Nonlinear Waves and Solitons on Contours and Closed Surfaces [electronic resource] /
Ludu, Andrei.author.
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 introduces the mathematical concept required for treating the manifolds considered. Emphasis on the 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. Nonlinear Waves and Solitons on Contours and Closed Surfaces provides graduate students and researchers in mathematics, physics and engineering with a ready tutorial and reference.
Description based upon print version of record.
Includes bibliographical references (p. 453-460) and index.
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.
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 introduces the mathematical concept required for treating the manifolds considered. Emphasis on the 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. Nonlinear Waves and Solitons on Contours and Closed Surfaces provides graduate students and researchers in mathematics, physics and engineering with a ready tutorial and reference.
Statistical physics.
Dynamical systems.
Dynamics.
Ergodic theory.
Mechanics.
Differential geometry.
Physics.
Fluids.
Complex Systems.
Dynamical Systems and Ergodic Theory.
Classical Mechanics.
Differential Geometry.
Mathematical Methods in Physics.
Fluid- and Aerodynamics.


Springer Series in Synergetics