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OverviewThe modem theory of solitons was born in 1967 when Gardner, Greene, Kruskal and Miura related the solution of the Cauchy initial value problem for the Korteweg-de Vries equation to the inverse scattering problem for a one dimensional linear Schroedinger equation. Soliton theory is now a large part of theoretical and mathematical physics. An important method used to solve related equations is based on the Inverse Scattering Transform (IST). This IST method has been extended and applied to a large variety of (analytically) solvable non linear evolution equations, including many important examples describing phe nomena in nonlinear optics, solid state physics, hydrodynamics, theory of general relativity, plasma physics, etc. In the about twenty years of development the necessary mathematical tools have become rather sophisticated. They include the methods of algebraic geome try, the machinery of group representations, the theory of the local and nonlocal Riemann-Hilbert problem and many other higher levels of contemporary math ematics. Full Product DetailsAuthor: Vladimir B. Matveev , Mikhail A. SallePublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Edition: Softcover reprint of the original 1st ed. 1991 ISBN: 9783662009246ISBN 10: 3662009242 Pages: 122 Publication Date: 30 September 1992 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of Contents1. Introduction.- 2. Darboux Transformations and Linear Equations.- 3. Exact Solutions of the KdV and KP Equations.- 4. Darboux Transformations for the Zero Curvature Equations and Nonlocal Nonlinear Evolution Equations.- 5. Nonlinear Lattice Equations and Related Systems.- 6. Darboux Transformation for 2+1 Nonlinear Evolution Equations and Localized Soliton Solutions.- 7. Hamiltonian Interpretation of the Darboux Transformations and Other Problems.- Comments on the Literature.- Summary and Outlook.- References.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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