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.
Nonlinear Waves and Solitons on Contours and Closed Surfaces
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Description
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.
Written for an interdisciplinary readership, this book is a practical guide to the fascinating world of solitons. The author approaches the subject from the standpoint of applications in optics, ...
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