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Direct and Inverse Methods in Nonlinear Evolution Equations

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Many physical phenomena are described by nonlinear evolution equation. Those that are integrable provide various mathematical meth... Weiterlesen
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Beschreibung

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.

Inhalt
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.

Produktinformationen

Titel: Direct and Inverse Methods in Nonlinear Evolution Equations
Untertitel: Lectures Given at the C.I.M.E. Summer School Held in Cetraro, Italy, September 5-12, 1999
Autor:
Editor:
EAN: 9783540200871
ISBN: 3540200878
Format: Fester Einband
Herausgeber: Springer Berlin Heidelberg
Genre: Mathematik
Anzahl Seiten: 292
Gewicht: 606g
Größe: H241mm x B160mm x T20mm
Jahr: 2003
Untertitel: Englisch
Auflage: 2003

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