Cauchy problem for nonlinear dispersive equations and integrable systems

2017 Fiscal Year Final Research Report

• Project/Area Number: 26800070
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Mathematical analysis
• Research Institution: Saga University
• Principal Investigator: Kato Takamori 佐賀大学, 工学(系)研究科(研究院), 講師 (50620639)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 非線形分散型 / 初期値問題 / 適切性 / 調和解析 / 可積分系

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.

Free Research Field

偏微分方程式論