On the behavior of solutions to some nonlinear Schrodinger equations

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400178
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical analysis
• Research Institution: Kumamoto University (2015); University of Miyazaki (2013-2014)
• Principal Investigator: Kita Naoyasu 熊本大学, 自然科学研究科, 教授 (70336056)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 非線形シュレディンガー方程式 / 解の漸近挙動 / 解の爆発

Outline of Final Research Achievements

I have reserched the asymptotic behaviors and blowing-up phenomena of solutions to the Cauchy problem for some nonlinear Schrodinger equations (NLS) which including complex coefficient in the nonlinearity. This kind of NLS describes shape change of puls - electro-magnetic wave - propagating through optical fibers. it is classified with the two cases - (1)nonlinear energy-dissipation and (2) nonlinear amplification. As results of my reserch supported by this national grant, in case (1), I specified the decay order of the solutions in the uniform norm even though the initial datum are attained without size-restriction. In addition, I could prove that the solutions are gradually minimized in L^2 norm as well. In case (2), the L^2-norm of the solutions blow up in finite time for small initial data.

Free Research Field

基礎解析