Nonlinear Waves and Solitons on Contours and Closed Surfaces by Ludu, Andrei;

Series: Springer Series in Synergetics;

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Product details:

Edition number Softcover reprint of hardcover 1st ed. 2007
Publisher Springer Berlin Heidelberg
Date of Publication 30 November 2010
Number of Volumes 1 pieces, Previously published in hardcover

ISBN 9783642091964
Binding Paperback
See also 9783540728726
No. of pages466 pages
Size 235x155 mm
Weight 741 g
Language English
Illustrations XX, 466 p. 140 illus. Illustrations, black & white

Categories

Geometry and topology Analysis Mathematics in engineering and natural sciences Taxonomy, systematics Physics in general Mechanics Thermodynamics and statistical physics Quantum physics (quantum mechanics) Astrophysics Further readings in the field of computing Further readings in physics Astronomy in general Geometry and topology (charity campaign) Analysis (charity campaign) Mathematics in engineering and natural sciences (charity campaign) Taxonomy, systematics (charity campaign) Physics in general (charity campaign) Mechanics (charity campaign) Thermodynamics and statistical physics (charity campaign) Quantum physics (quantum mechanics) (charity campaign) Astrophysics (charity campaign) Further readings in the field of computing (charity campaign) Further readings in physics (charity campaign) Astronomy in general (charity campaign)

Long description:

Everything the Power of the World does is done in a circle. The sky is round and I have heard that the earth is round like a ball and so are all the stars. The wind, in its greatest power, whirls. Birds make their nests in circles, for theirs is the same religion as ours. The sun comes forth and goes down again in a circle. The moon does the same and both are round. Even the seasons form a great circle in their changing and always come back again to where they were. The life of a man is a circle from childhood to childhood. And so it is everything where power moves. Black Elk (1863–1950) Nonlinearity is a captivating manifestation of the observable Universe, whose importance has increased over the decades, and has found more and more ?elds of application ranging from elementary particles, nuclear physics, biology, wave dynamics at any scale, ?uids, plasmas to astrophysics. The central character of this 172-year-old story is the soliton. Namely, a localized pulse traveling without spreading and having particle-like properties plus an in?nite number of conservation laws associated to its dynamics. In general, solitons arise as exact solutions of approximative models. There are di?- ent explanation, at di?erent levels, for the existence of solitons. From the experimentalist point of view, solitons can be created if the propagation c- ?gurationislongenough,narrowenough(likelongandshallowchannels,?ber optics, electric lines, etc.

More

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.