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 (Lecture Notes in Physics, Band 632) - Softcover

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

Softcover

ISBN 10: 3642057535 ISBN 13: 9783642057533

Verlag: Springer, 2010

Inhaltsangabe

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.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2010
• Sprache: Englisch
• ISBN 10: 3642057535
• ISBN 13: 9783642057533
• Einband: Taschenbuch
• Anzahl der Seiten: 292
• Herausgeber: Greco Antonio Maria
• Kontakt zum Hersteller: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Deutschland