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Table of contents (5 chapters)
Keywords
About this book
Many physical phenomena are described by nonlinear evolution equation. Those that are integrable provide various mathematical methods, presented by experts in this tutorial book, to find special analytic solutions to both integrable and partially integrable equations. The direct method to build solutions includes the analysis of singularities à la Painlevé, Lie symmetries leaving the equation invariant, extension of the Hirota method, construction of the nonlinear superposition formula. The main inverse method described here relies on the bi-hamiltonian structure of integrable equations. The book also presents some extension to equations with discrete independent and dependent variables.
The different chapters face from different points of view the theory of exact solutions and of the complete integrability of nonlinear evolution equations. Several examples and applications to concrete problems allow the reader to experience directly the power of the different machineries involved.
Authors, Editors and Affiliations
Bibliographic Information
Book Title: Direct and Inverse Methods in Nonlinear Evolution Equations
Book Subtitle: Lectures Given at the C.I.M.E. Summer School Held in Cetraro, Italy, September 5–12, 1999
Authors: Robert M. Conte, Franco Magri, Micheline Musette, Junkichi Satsuma, Pavel Winternitz
Editors: Antonio Maria Greco
Series Title: Lecture Notes in Physics
DOI: https://doi.org/10.1007/b13714
Publisher: Springer Berlin, Heidelberg
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 2003
Hardcover ISBN: 978-3-540-20087-1Published: 21 October 2003
Softcover ISBN: 978-3-642-05753-3Published: 09 December 2010
eBook ISBN: 978-3-540-39808-0Published: 23 September 2003
Series ISSN: 0075-8450
Series E-ISSN: 1616-6361
Edition Number: 1
Number of Pages: XI, 279
Topics: Mathematical Methods in Physics, Partial Differential Equations, Differential Geometry, Complex Systems, Statistical Physics and Dynamical Systems