2011 Fiscal Year Final Research Report
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 |
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| Research Field |
Basic analysis
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| Research Institution | Tohoku University |
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Principal Investigator |
FUKUIZUMI Reika 東北大学, 大学院・情報科学研究科, 准教授 (00374182)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 関数方程式論 / 解析学 / 確率論 / 数理物理 |
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| 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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