Direct and inverse methods in nonlinear evolution equations : lectures given at the C.I.M.E. summer school held in Cetraro, Italy, September 5-12, 1999 /

Direct and inverse methods in nonlinear evolution equations : lectures given at the C.I.M.E. summer school held in Cetraro, Italy, September 5-12, 1999 /

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Bibliographic Details
Imprint:Berlin ; New York : Springer, ©2003.
Description:1 online resource (xi, 278 pages) : illustrations.
Language:English
Series:Lecture notes in physics, 0075-8450 ; 632
Lecture notes in physics ; 632.
Subject:
Evolution equations, Nonlinear -- Numerical solutions -- Congresses.
Inverse problems (Differential equations) -- Numerical solutions -- Congresses.
Evolution equations, Nonlinear -- Numerical solutions.
Inverse problems (Differential equations) -- Numerical solutions.
Conference papers and proceedings.
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/11069408
Hidden Bibliographic Details
Other authors / contributors:Conte, Robert, 1943-
Greco, Antonio M.
ISBN:9783540398080
3540398082
3540200878
9783540200871
Notes:Includes bibliographical references (pages 263-273) and index.
Summary: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 la Painlev, 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.
Other form:Print version: Direct and inverse methods in nonlinear evolution equations. Berlin ; New York : Springer, ©2003 3540200878

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