Stability of solitary waves for nonlinear dispersive equations
Project/Area Number |
21740089
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Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Single-year Grants |
Research Field |
Basic analysis
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Research Institution | Tohoku University |
Principal Investigator |
FUKUIZUMI Reika 東北大学, 大学院・情報科学研究科, 准教授 (00374182)
|
Project Period (FY) |
2009 – 2011
|
Project Status |
Completed (Fiscal Year 2011)
|
Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2009: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
|
Keywords | 関数方程式論 / 解析学 / 確率論 / 数理物理 / 偏微分方程式 / 非線形Schrodinger方程式 / 定常解の安定性 / 変分解析 / 確率微分方程式 |
Research Abstract |
Concerning a model for the Bose-Einstein Condensation trapped under an optical confinement involving fluctuations by laser frequencies, I justified mathematically the existence of solution constructing the fundamental solution of linear stochastic Schrodinger equations, and proved a long time behavior of stable standing waves influenced by temporal white noise. On the other hand, I investigated the stability of excited states for a model which describes the propagation of laser beam in the hollow-core fibers. As for a model of optic fibers, I showed the symmetry breaking of ground state for the case where two symmetric defects are present in the medium.
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Report
(4 results)
Research Products
(15 results)