2014 Fiscal Year Final Research Report
Dynamics of the Gross-Pitaevskii equation and related problems
| Project/Area Number |
24740079
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | Tohoku University |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Keywords | 偏微分方程式論 / 確率論 |
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| Outline of Final Research Achievements |
The Gross-Pitaevskii equation perturbed by (only temporal) white noise is considered. In particular, we analyzed the modulation parameters in a stable vortex solution and we estimated how long those modulation parameters can have a meaning compared to the noise, that is, how long the stable vortex input initially can persist its form compared to the strength of the noise. On the other hand, with the use of semi-classical technique, we justified the approximation of the wave function of the Gross-Pitaevskii equation trapped in a periodic potential via the solution of the associated discrete nonlinear Schroedinger equation. As an application of this approximation, we showed the localization of the wave function even if defocusing nonlinearities are considered.
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| Free Research Field |
解析学
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