ENGLISH

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

By Robert Conte (auth.)

Book information

Publisher
Springer Berlin Heidelberg
Year
2003
ISBN
3540200878, 9783540200871
DOI
10.1007/b13714
ISSN
0075-8450
Open Library ID
OL9054357M
Language
english
Format
DJVU
Filesize
1 MB (1164956 bytes)
Series
Lecture Notes in Physics 632
Edition
1
Pages
XI, 279 p.\287
Library
Kolxo3
DPI
300
Scanned
yes
Time added
2009-07-20 03:45:11

Description

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 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.

Similar books