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Hamiltonian Methods in the Theory of Solitons

Ludwig Faddeev, Leon Takhtajan (Autoren)

Buch | Softcover

IX, 592 Seiten

2007 | 1. Reprint of the 1st ed. Berlin Heidelberg New York 1987
Springer Berlin (Verlag)
978-3-540-69843-2 (ISBN)

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This book presents the foundations of the inverse scattering method and its applications to the theory of solitons in such a form as we understand it in Leningrad. The concept of solitonwas introduced by Kruskal and Zabusky in 1965. A soliton (a solitary wave) is a localized particle-like solution of a nonlinear equation which describes excitations of finite energy and exhibits several characteristic features: propagation does not destroy the profile of a solitary wave; the interaction of several solitary waves amounts to their elastic scat tering, so that their total number and shape are preserved. Occasionally, the concept of the soliton is treated in a more general sense as a localized solu tion of finite energy. At present this concept is widely spread due to its universality and the abundance of applications in the analysis of various processes in nonlinear media. The inverse scattering method which is the mathematical basis of soliton theory has developed into a powerful tool of mathematical physics for studying nonlinear partial differential equations, almost as vigoraus as the Fourier transform. The book is based on the Hamiltonian interpretation of the method, hence the title. Methods of differential geometry and Hamiltonian formal ism in particular are very popular in modern mathematical physics. It is precisely the general Hamiltonian formalism that presents the inverse scat tering method in its most elegant form. Moreover, the Hamiltonian formal ism provides a link between classical and quantum mechanics.

Ludwig D. Faddeev was born in Leningrad, USSR in 1934. He graduated from the Leningrad State University in 1956 and received his Ph.D. from there in 1959. Since 1959 he has been affiliated with the Leningrad branch of Steklov Mathematical Institute and was its Director from 1976 to 2000. Currently Faddeev is Director of the Euler International Mathematical Institute in St. Petersburg, Russia, and Academician-Secretary of the Mathematics Division of the Russian Academy of Sciences. He was President of the International Mathematical Union during1986-1990.

The Nonlinear Schrödinger Equation (NS Model).- Zero Curvature Representation.- The Riemann Problem.- The Hamiltonian Formulation.- General Theory of Integrable Evolution Equations.- Basic Examples and Their General Properties.- Fundamental Continuous Models.- Fundamental Models on the Lattice.- Lie-Algebraic Approach to the Classification and Analysis of Integrable Models.- Conclusion.- Conclusion.

Erscheint lt. Verlag	18.5.2007
Reihe/Serie	Classics in Mathematics
Übersetzer	A.G. Reyman
Zusatzinfo	IX, 592 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	920 g
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	Curvature • Integrable Evolution Equations • inverse scattering method • Lie-Algebra • Mathematische Physik • Partial differential equations • Riemann problem • Schrödinger equations • Soliton
ISBN-10	3-540-69843-4 / 3540698434
ISBN-13	978-3-540-69843-2 / 9783540698432
Zustand	Neuware