| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Outline of Final Research Achievements |
We studied the well-poseness for the Cauchy problem of the periodic fifth order KdV equation and fifth order modified KdV equation which are completely integrable. In this study, the key idea is how to analysis the resonant parts in which the strongest nonlinear interaction concentrates. We succeeded in giving the explicit formula of the resonant pars and cancelling them by using the algebraic structure of integrable systems. Moreover, since the nonlinear terms except resonant parts were able to be regarded as the perturbation of the linearized solutions, we proved the well-posedness and unconditional uniqueness in wide function spaces.
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