| 书目名称 | Direct and Inverse Methods in Nonlinear Evolution Equations |
| 副标题 | Lectures Given at th |
| 编辑 | Robert M. Conte,Franco Magri,Pavel Winternitz,Anto |
| 视频video | |
| 丛书名称 | Lecture Notes in Physics |
| 图书封面 |  |
| 描述 | .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.. |
| 出版日期 | Book 2003 |
| 关键词 | Lax Pair; Lie Symmetries; Painlevé Analysis; Poison Pair; Singularity Analysis; calculus; differential equ |
| 版次 | 1 |
| doi | https://doi.org/10.1007/b13714 |
| isbn_softcover | 978-3-642-05753-3 |
| isbn_ebook | 978-3-540-39808-0Series ISSN 0075-8450 Series E-ISSN 1616-6361 |
| issn_series | 0075-8450 |
| copyright | Springer-Verlag Berlin Heidelberg 2003 |
发表于 2025-3-21 17:40:49
