Long time oscillation of solutions of nonlinear Schrodinger equations near minimal mass ground state
Long time oscillation of solutions of nonlinear Schrodinger equations near minimal mass ground state
复制标题
非线性薛定谔方程解在最小质量基态附近的长时间振荡
DOI：
10.1016/j.jde.2019.11.047
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发表时间：
2020
影响因子：
2.4
通讯作者：
Maeda Masaya
中科院分区：
文献类型：
--
作者：
Cuccagna Scipio;Maeda Masaya
在本文中，我们考虑具有最小质量基态的非线性薛定谔方程（NLS）的径向对称解的长期动力学。特别是，我们表明存在初始数据接近最小质量基态且长时间振荡的解。更准确地说，我们引入了一个在最小质量基态附近定义的坐标，该坐标由与线性算子的离散和连续部分相关的有限和无限维部分组成。然后，我们证明有限维（2-D）部分近似服从非谐势阱中粒子的牛顿运动方程。表明无限维部分与有限维部分很好地分离，我们将出现长时间振荡。
In this paper, we consider the long time dynamics of radially symmetric solutions of nonlinear Schrödinger equations (NLS) having a minimal mass ground state. In particular, we show that there exist solutions with initial data near the minimal mass ground state that oscillate for long time. More precisely, we introduce a coordinate defined near the minimal mass ground state which consists of finite and infinite dimensional part associated to the discrete and continuous part of the linearized operator. Then, we show that the finite dimensional (2–D) part approximately obeys Newton's equation of motion for a particle in an anharmonic potential well. Showing that the infinite dimensional part is well separated from the finite dimensional part, we will have long time oscillation.