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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| Imprint: | Berlin ; New York : Springer, ©2003. |
|---|---|
| Description: | 1 online resource (xi, 278 pages) : illustrations. |
| Language: | English |
| Series: | Lecture notes in physics, 0075-8450 ; 632 Lecture notes in physics ; 632. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11069408 |
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| 245 | 0 | 0 | |a Direct and inverse methods in nonlinear evolution equations : |b lectures given at the C.I.M.E. summer school held in Cetraro, Italy, September 5-12, 1999 / |c R. Conte [and others] ; editor, Antonio M. Greco. |
| 260 | |a Berlin ; |a New York : |b Springer, |c ©2003. | ||
| 300 | |a 1 online resource (xi, 278 pages) : |b illustrations. | ||
| 336 | |a text |b txt |2 rdacontent |0 http://id.loc.gov/vocabulary/contentTypes/txt | ||
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| 490 | 1 | |a Lecture notes in physics, |x 0075-8450 ; |v 632 | |
| 504 | |a Includes bibliographical references (pages 263-273) and index. | ||
| 505 | 0 | |a 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. | |
| 520 | |a 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. | ||
| 650 | 0 | |a Evolution equations, Nonlinear |x Numerical solutions |v Congresses. | |
| 650 | 0 | |a Inverse problems (Differential equations) |x Numerical solutions |v Congresses. | |
| 650 | 7 | |a Evolution equations, Nonlinear |x Numerical solutions. |2 fast |0 (OCoLC)fst00917336 | |
| 650 | 7 | |a Inverse problems (Differential equations) |x Numerical solutions. |2 fast |0 (OCoLC)fst00978099 | |
| 655 | 4 | |a Electronic books. | |
| 655 | 7 | |a Conference papers and proceedings. |2 fast |0 (OCoLC)fst01423772 | |
| 700 | 1 | |a Conte, Robert, |d 1943- |0 http://id.loc.gov/authorities/names/n90621844 |1 http://viaf.org/viaf/34571708 | |
| 700 | 1 | |a Greco, Antonio M. |0 http://id.loc.gov/authorities/names/nr98025675 |1 http://viaf.org/viaf/71689002 | |
| 776 | 0 | 8 | |i Print version: |t Direct and inverse methods in nonlinear evolution equations. |d Berlin ; New York : Springer, ©2003 |z 3540200878 |w (DLC) 2003055841 |w (OCoLC)52902747 |
| 830 | 0 | |a Lecture notes in physics ; |v 632. |x 0075-8450 | |
| 856 | 4 | 0 | |u http://link.springer.com/10.1007/b13714 |y SpringerLink |
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