Singularity analysis on the nonlinear Schrodinger equations
| Project/Area Number |
20540181
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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 | University of Miyazaki |
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Principal Investigator |
KITA Naoyasu 宮崎大学, 教育文化学部, 准教授 (70336056)
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| Project Period (FY) |
2008 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 非線形現象 / 非線形偏微分方程式 / シュレディンガー方程式 / 解の適切性 / 非線形Schrodinger方程式 / 非線形シュレディンガー方程式 / 解の非適切性 / 解の漸近挙動 / 解の減衰評価 |
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| Research Abstract |
We obtained the global existence and non-existence of the solutions to the Cauchy problem of nonlinear Schrodinger equations. Remark that, in our research, the initial data consists of superposition of d-functions. In particular, when the initial data consists of three d-functions, we observe that the difficulty of the proof for global existence changes dependently on the distribution of the d-functions. Furthermore, giving a concrete distribution like d-functions, we see that certain feature of solutions, e.g., generalization of new modes, which is typically caused by nonlinear phenomena.
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Report
(7 results)
Research Products
(19 results)
