2009 Fiscal Year Final Research Report
Study on the instability of Benjamin-Feir type concerned with nonlinear strongly dispersive systems
| Project/Area Number |
19540232
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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 |
Global analysis
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| Research Institution | Doshisha University |
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Principal Investigator |
OHMIYA Mayumi Doshisha University, 生命医科学部, 教授 (50035698)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 強分散系 / 定常KdV階層 / 第一積分 / 跡公式 / ソリトン / 不安定現象 / イジング模型 / サイン-ゴードン方程式 |
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| Research Abstract |
The first order approximate solution of Fourier type is constructed for the Sine-Gordon equation, which is the typical example of strongly dispersive nonlinear system, and its instability of Benjamine-Feir type is clarified by Floquet theory. Furthermore, to clarify the instability phenomena of general strongly dispersive nonlinear system, to begin with, various methods of constructing first integrals have been developed for weakly dispersive nonlinear system such as nonlinear equations of KdV type. Moreover, the relations between the higher order stationary KdV equation and the trace formulas have been clarified, and it is uniformly proved that the rapidly decreasing Bargmann potentials and the periodic finite zonal potentials solve the higher order stationary KdV equations. Simultaneously, to find the dispersive property for the given microscopic system, a numerical method called Baby-Bathwater scheme is studied. On the one hand, mechanism of critical phenomena has been clarified for complex network system by numerical methods.
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