2010 Fiscal Year Final Research Report
Scattering theory for linear and nonlinear Schrodinger equations
| Project/Area Number |
20540169
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kobe University |
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Principal Investigator |
ADACHI Tadayoshi Kobe University, 大学院・理学研究科, 教授 (30281158)
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| Co-Investigator(Kenkyū-buntansha) |
TAKAOKA Hideo 北海道大学, 大学院・理学研究院, 教授 (10322794)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 多体問題 / スペクトル理論 / 散乱理論 / 漸近完全性 / 電磁場 / 時間大域的適切性 |
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| Research Abstract |
The achievements of our research are as follows: 1. We improved some results obtained by several previous works on the asymptotic completeness for quantum systems in time-dependent homogeneous electric fields. 2. We obtained a new result on a certain problem of the inverse scattering for quantum systems in homogeneous electric fields asymptotically zero in time. 3. We obtained new results on the problems of the well-posedness and the scattering theory for various nonlinear dispersive equations, especially in critical cases.
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