| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Outline of Final Research Achievements |
We investigated the spatially periodic solutions of nonlinear dispersive partial differential equations arising as important models in various fields of physics and engineering. In particular, we studied unconditional uniqueness for the initial value problem, namely, uniqueness of solutions in a natural class. We succeeded in providing a general framework applicable to a wide range of nonlinear dispersive equations, and applied it to some specific problems for which unconditional uniqueness had been open. Moreover, for the nonlinear Schroedinger equation and an equation for rotating fluids, we analyzed the interactions between resonant frequencies, which seem important in controlling the nonlinear interactions, by use of some techniques from combinatorics and elementary number theory.
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