| Budget Amount *help |
¥16,250,000 (Direct Cost: ¥12,500,000、Indirect Cost: ¥3,750,000)
Fiscal Year 2017: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2016: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2015: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2014: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2013: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
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| Outline of Final Research Achievements |
In this study, I have developed the local and global well-posedness for the initial value problem related to the nonlinear Schrodinger equations in which dispersion effect and nonlinear interaction effect are incorporating. Using the Fourier analysis, I separated the solution into two parts; non-resonant and resonant oscillation parts, which have different in nature and distinguish nonuniformity part of solutions. For the nonlinear Schrodinger equations both with derivative in nonlinearities and on a sphere domain, I improved the local well-posedness for large function spaces. Moreover, I showed that there exists exchange of energy between Fourier modes. In the research process, I observed the estimation of energy exchange between different Fourier modes, due to the contribution in the nonlinear interaction.
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