| 书目名称 | Korteweg–de Vries Flows with General Initial Conditions |
| 编辑 | Shinichi Kotani |
| 视频video | http://file.papertrans.cn/541/540005/540005.mp4 |
| 概述 | Presents a new method to solve the KdV equation starting from decaying or oscillating initial data.Enables the treatment of ergodic (including almost periodic) initial data, which may generate dense s |
| 丛书名称 | Mathematical Physics Studies |
| 图书封面 |  |
| 描述 | .Large numbers of studies of the KdV equation have appeared since the pioneering paper by Gardner, Greene, Kruskal, and Miura in 1967. Most of those works have employed the inverse spectral method for 1D Schrödinger operators or an advanced Fourier analysis. Although algebraic approaches have been discovered by Hirota–Sato and Marchenko independently, those have not been fully investigated and analyzed.. .The present book offers a new approach to the study of the KdV equation, which treats decaying initial data and oscillating data in a unified manner. The author’s method is to represent the tau functions introduced by Hirota–Sato and developed by Segal–Wilson later in terms of the Weyl–Titchmarsh functions (WT functions, in short) for the underlying Schrödinger operators. The main result is stated by a class of WT functions satisfying some of the asymptotic behavior along a curve approaching the spectrum of the Schrödinger operators at +∞ in an order of -(.n.-1/2)for the .n.th KdV equation. This class contains many oscillating potentials (initial data) as well as decaying ones. Especially bounded smooth ergodic potentials are included, and under certain conditions on the potential |
| 出版日期 | Book 2024 |
| 关键词 | KdV Equation; Schrödinger Operator; Tau Function; Weyl-Titchmarsh Function; Ergodic Schrödinger Operator |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-981-99-9738-1 |
| isbn_softcover | 978-981-99-9740-4 |
| isbn_ebook | 978-981-99-9738-1Series ISSN 0921-3767 Series E-ISSN 2352-3905 |
| issn_series | 0921-3767 |
| copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapor |
|Archiver|手机版|小黑屋|
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