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: 632 - Rilegato

Conte, Robert; Magri, Franco; Musette, Micheline; Satsuma, Junkichi; Winternitz, Pavel

 
9783540200871: 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: 632
Rilegato
ISBN 10: 3540200878 ISBN 13: 9783540200871
Casa editrice: Springer Verlag, 2003

Sinossi

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.

Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.

Contenuti

Exact Solutions of Nonlinear Partial Differential Equations by Singularity Analysis.- The Method of Poisson Pairs in the Theory of Nonlinear PDEs.- Nonlinear Superposition Formulae of Integrable Partial Differential Equations by the Singular Manifold Method.- Hirota Bilinear Method for Nonlinear Evolution Equations.- Lie Groups, Singularities and Solutions of Nonlinear Partial Differential Equations.

Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.

Editore
Springer Verlag
Data di pubblicazione
2003
Lingua
Inglese
ISBN 10 
3540200878
ISBN 13 
9783540200871
Rilegatura
Copertina rigida
Numero di pagine
278
Redattore
Greco Antonio M., Magri Franco, Musette Micheline, Satsuma Junkichi, Winternitz Pavel, Conte Robert
Contatto del produttore
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Altre edizioni note dello stesso titolo

9783642057533: 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: 632

Edizione in evidenza

ISBN 10:  3642057535 ISBN 13:  9783642057533
Casa editrice: Springer, 2010
Brossura