| 书目名称 | The Painlevé Handbook | | 编辑 | Robert Conte,Micheline Musette | | 视频video | | | 概述 | Thorough treatment of the Painlevé property and Painlevé tests of differential equations.With many worked examples illustrating the methods developed.Written at a level accessible to graduate students | | 图书封面 |  | | 描述 | .Nonlinear differential or difference equations are encountered not only in mathematics, but also in many areas of physics (evolution equations, propagation of a signal in an optical fiber), chemistry (reaction-diffusion systems), and biology (competition of species)...This book introduces the reader to methods allowing one to build explicit solutions to these equations. A prerequisite task is to investigate whether the chances of success are high or low, and this can be achieved without any a priori knowledge of the solutions, with a powerful algorithm presented in detail called the Painlevé test. If the equation under study passes the Painlevé test, the equation is presumed integrable. If on the contrary the test fails, the system is nonintegrable or even chaotic, but it may still be possible to find solutions...The examples chosen to illustrate these methods are mostly taken from physics. These include on the integrable side the nonlinear Schrödinger equation (continuous and discrete), the Korteweg-de Vries equation, the Hénon-Heiles Hamiltonians, on the nonintegrable side the complex Ginzburg-Landau equation (encountered in optical fibers, turbulence, etc), the Kuramoto-Sivashi | | 出版日期 | Book 20081st edition | | 关键词 | Canopus; Nevanlinna theory; Painlevé test; Schrödinger equation; Signal; Soliton; algorithm; closed form so | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4020-8491-1 | | isbn_softcover | 978-94-007-9627-0 | | isbn_ebook | 978-1-4020-8491-1 | | copyright | Springer Science+Business Media B.V. 2008 |
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发表于 2025-3-21 17:43:49
