Direct and Inverse Methods in Nonlinear Evolutions Equations

Lectures Given at the C. I. M. E. Summer School Held in Cetraro, Italy, September 5-12 1999

By: Robert M. Conte, Antonio Maria Greco (Editor), Franco Magri

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Hardcover | 1 January 2004

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296 Pages

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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 Painlev©, 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.

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Differential Calculus & Equations Geometry Differential & Riemannian Geometry Science Physics Mathematical Physics

Exact solutions of nonlinear partial differential equations by singularity analysis	p. 1
The method of Poisson pairs in the theory of nonlinear PDEs	p. 85
Nonlinear superposition formulae of integrable partial differential equations by the singular manifold method	p. 137
Hirota bilinear method for nonlinear evolution equations	p. 171
Lie groups, singularities and solutions of nonlinear partial differential equations	p. 223
List of Participants	p. 274
Index	p. 277
Table of Contents provided by Blackwell. All Rights Reserved.

Direct and Inverse Methods in Nonlinear Evolutions Equations

Lectures Given at the C. I. M. E. Summer School Held in Cetraro, Italy, September 5-12 1999

At a Glance

Hardcover

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How to return your order

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