Nonlinear Waves and Solitons on Contours and Closed Surfaces
Springer Berlin (Verlag)
978-3-540-72872-6 (ISBN)
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The first part of the book introduces the mathematical concept required for treating the manifolds considered. An introduction to the theory of motion of curves and surfaces is given. The second and third parts discuss the modeling of various physical solitons on compact systems.
Nonlinear and solitary waves are historically related to quasi one-dimensional systems where the spatial extent in one direction is much bigger than in the other direction, such as channels and fibres. The present book treats the case of more compact systems and their nonlinear ascillations, which have only recently come into forms. Such systems include liquid drop models, Bose-Einstein condensates and even living cells. A general formalism is developed, based on the differential geometry of curved manifolds, and various applications are considered in the physical sciences and beyond.
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.
Erscheint lt. Verlag | 14.4.2009 |
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Reihe/Serie | Springer Series in Synergetics |
Sprache | englisch |
Maße | 155 x 235 mm |
Einbandart | gebunden |
Themenwelt | Naturwissenschaften ► Physik / Astronomie ► Astronomie / Astrophysik |
Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik | |
Schlagworte | closed curves • contour dynamics • Nonlinear waves • Solitons • Surface Waves |
ISBN-10 | 3-540-72872-4 / 3540728724 |
ISBN-13 | 978-3-540-72872-6 / 9783540728726 |
Zustand | Neuware |
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