NonlinearWaves and Solitons on Contours and Closed Surfaces

Part I. Mathematical Prerequisites

1. Introduction

2. Mathematical Prerequisites

3. The Importance of the Boundary

4. Vector Fields, Differential Forms, and Derivatives

5. Geometry of Curves

6. Motion of Curves and Solitons

7. Geometry of Surfaces

8. Theory of Motion of Surfaces

Part II. Solitons and Nonlinear Waves on Closed Curves and Surfaces

9. Kinematics of Hydrodynamics

10. Dynamics of Hydrodynamics

11. Nonlinear Surface Waves in One Dimension

12. Nonlinear Surface Waves in Two Dimensions

13. Nonlinear Surface Waves in Three Dimensions

14. Other Special Nonlinear Compact Systems

Part III. Physical Nonlinear Systems at Different Scales

15. Filaments, Chains, and Solitons

16. Solitons on the Boundaries of Microscopic Systems

17. Nonlinear Contour Dynamics in Macroscopic Systems

18. Mathematical Annex

DRM-restrictions

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Keywords: SCIENCE / Physics SCI055000