On the behavior of solutions to some nonlinear Schrodinger equations
| Project/Area Number |
25400178
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Mathematical analysis
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| Research Institution | Kumamoto University (2015)
University of Miyazaki (2013-2014) |
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Principal Investigator |
Kita Naoyasu 熊本大学, 自然科学研究科, 教授 (70336056)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 非線形シュレディンガー方程式 / 解の漸近挙動 / 解の爆発 / 非線形消散項 / 非線形増幅項 / 解の減衰評価 / 漸近挙動 |
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| Outline of Final Research Achievements |
I have reserched the asymptotic behaviors and blowing-up phenomena of solutions to the Cauchy problem for some nonlinear Schrodinger equations (NLS) which including complex coefficient in the nonlinearity. This kind of NLS describes shape change of puls - electro-magnetic wave - propagating through optical fibers. it is classified with the two cases - (1)nonlinear energy-dissipation and (2) nonlinear amplification. As results of my reserch supported by this national grant, in case (1), I specified the decay order of the solutions in the uniform norm even though the initial datum are attained without size-restriction. In addition, I could prove that the solutions are gradually minimized in L^2 norm as well. In case (2), the L^2-norm of the solutions blow up in finite time for small initial data.
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Report
(4 results)
Research Products
(3 results)
