| 书目名称 | KdV & KAM |
| 编辑 | Thomas Kappeler,Jürgen Pöschel |
| 视频video | |
| 概述 | This text treats the Korteweg-de Vries (KdV) equation with periodic boundary conditions.For the first time these important results are comprehensively covered in book form.The authors are internationa |
| 丛书名称 | Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathemati |
| 图书封面 |  |
| 描述 | .In this text the authors consider the Korteweg-de Vries (KdV) equation (u.t. = - u.xxx. + 6uu.x.) with periodic boundary conditions. Derived to describe long surface waves in a narrow and shallow channel, this equation in fact models waves in homogeneous, weakly nonlinear and weakly dispersive media in general...Viewing the KdV equation as an infinite dimensional, and in fact integrable Hamiltonian system, we first construct action-angle coordinates which turn out to be globally defined. They make evident that all solutions of the periodic KdV equation are periodic, quasi-periodic or almost-periodic in time. Also, their construction leads to some new results along the way. ..Subsequently, these coordinates allow us to apply a general KAM theorem for a class of integrable Hamiltonian pde‘s, proving that large families of periodic and quasi-periodic solutions persist under sufficiently small Hamiltonian perturbations. ..The pertinent nondegeneracy conditions are verified by calculating the first few Birkhoff normal form terms -- an essentially elementary calculation. . |
| 出版日期 | Book 2003 |
| 关键词 | Calculation; Finite; Integrable Systems; KAM Theory; KdV Equation; Perturbation Theory; equation; function; |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-662-08054-2 |
| isbn_softcover | 978-3-642-05694-9 |
| isbn_ebook | 978-3-662-08054-2Series ISSN 0071-1136 Series E-ISSN 2197-5655 |
| issn_series | 0071-1136 |
| copyright | Springer-Verlag Berlin Heidelberg 2003 |
发表于 2025-3-21 16:40:33
