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 |
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| Editor:
| Greco, Antonio Maria |
| Author:
| Magri, Franco
Musette, Micheline
Satsuma, Junkichi
Winternitz, Pavel
Conte, Robert M. |
| Series title: | Lecture Notes in Physics Ser. |
| ISBN: | 978-3-540-20087-1 |
| Publication Date: | Jan 2003 |
| Publisher: | Springer
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| Book Format: | Hardback |
| List Price: | AUD $276.95 |
Book Description:
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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 à la Painlevé, Lie symmetries leaving the equation invariant, extension of the Hirota method, construction of the nonlinear superposition...
More Description
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.