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.
| ISBN: | 9783642057533 |
| Publication date: | 9th December 2010 |
| Author: | Robert Conte, Antonio M Greco |
| Publisher: | Springer an imprint of Springer Berlin Heidelberg |
| Format: | Paperback |
| Pagination: | 278 pages |
| Series: | Lecture Notes in Physics |
| Genres: |
Mathematical physics Cybernetics and systems theory Differential calculus and equations Differential and Riemannian geometry |
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.
Direct and Inverse Methods in Nonlinear Evolution Equations features in the following genres: Mathematical physics, Cybernetics and systems theory, Differential calculus and equations, Differential and Riemannian geometry
Direct and Inverse Methods in Nonlinear Evolution Equations is available in Paperback
Direct and Inverse Methods in Nonlinear Evolution Equations was written by Robert Conte, Antonio M Greco and published by Springer an imprint of Springer Berlin Heidelberg
Direct and Inverse Methods in Nonlinear Evolution Equations has 278 pages
Yes it is part of Lecture Notes in Physics series