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
Author:   Robert M. Conte ,  Antonio Maria Greco ,  Franco Magri ,  Micheline Musette
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Edition:   2003 ed.
Volume:   632
ISBN:  

9783540200871


Pages:   279
Publication Date:   21 October 2003
Format:   Hardback
Availability:   In Print   Availability explained
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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


Overview

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 a la Painleve, 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.

Full Product Details

Author:   Robert M. Conte ,  Antonio Maria Greco ,  Franco Magri ,  Micheline Musette
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   2003 ed.
Volume:   632
Dimensions:   Width: 15.50cm , Height: 1.70cm , Length: 23.50cm
Weight:   1.310kg
ISBN:  

9783540200871


ISBN 10:   3540200878
Pages:   279
Publication Date:   21 October 2003
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print   Availability explained
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of Contents

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.

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