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
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.

1139935478
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
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.

109.99 In Stock
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

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

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

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 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.

Product Details

ISBN-13: 9783642057533
Publisher: Springer Berlin Heidelberg
Publication date: 12/09/2010
Series: Lecture Notes in Physics , #632
Edition description: Softcover reprint of the original 1st ed. 2003
Pages: 279
Product dimensions: 6.10(w) x 9.25(h) x (d)

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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