• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to project page

2015 Fiscal Year Final Research Report

Existence and global behavior of spatially periodic solutions to the initial value problems for nonlinear dispersive equations

Research Project

  • PDF
Project/Area Number 24740086
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Basic analysis
Research InstitutionKyoto University

Principal Investigator

Kishimoto Nobu  京都大学, 数理解析研究所, 講師 (90610072)

Project Period (FY) 2012-04-01 – 2016-03-31
Keywords非線形分散型方程式 / 初期値問題 / 適切性 / 周期境界条件 / 無条件一意性
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.

Free Research Field

非線形偏微分方程式

URL: 

Published: 2017-05-10  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi