Final state problem for nonlinear Schr?dinger equations with time-decaying harmonic oscillators
Final state problem for nonlinear Schr?dinger equations with time-decaying harmonic oscillators
复制标题
具有时间衰减谐振子的非线性薛定谔方程的终态问题
DOI：
10.1016/j.jmaa.2021.125292
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发表时间：
2021
影响因子：
1.3
通讯作者：
Kawamoto Masaki
中科院分区：
文献类型：
--
作者：
小鳥居 祐香;水澤 篤彦;Kawamoto Masaki
本文研究了具有适当时衰谐振子的非线性薛定谔方程的终态问题。在这个方程中，非线性的力量|u|如果0 ≤ λ< 1/2，0< ρ≤ 2/（n（1− λ）），ρ u包含在长程类中，这由调和势和拉普拉斯算子的系数决定。在本文中，我们找到了该系统的最终状态，并获得了渐近的衰减估计。
We consider the final-state problem for the nonlinear Schrödinger equations (NLS) with a suitable time-decaying harmonic oscillator. In this equation, the power of nonlinearity| u| ρ u is included in the long-range class if 0< ρ≤ 2/(n (1− λ)) with 0≤ λ< 1/2, which is determined by the harmonic potential and a coefficient of Laplacian. In this paper, we find the final state for this system and obtain the decay estimate for asymptotics.