2012 Fiscal Year Final Research Report
Global analysis of dispersion and resonance of nonlinear waves
| Project/Area Number |
21740095
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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 | Kyoto University |
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Principal Investigator |
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| Project Period (FY) |
2009 – 2012
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| Keywords | 関数方程式 / 関数解析 / 実解析 |
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| Research Abstract |
I constructed a theory to determine space-time behavior of general solutions for partial differential equations describing nonlinear waves, from the initial data and topological information on the solution in the phase space, and completely classified space-time dynamics up to an energy level slightly above that of the ground state. It is a mathematically rigorous description, based solely on the equation, of the mechanism of scattering, soliton and blow-up, which are typical behavior of nonlinear waves, and of transitions among them.
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