Failure of scattering to standing waves for a Schr?dinger equation with long-range nonlinearity on star graph
Failure of scattering to standing waves for a Schr?dinger equation with long-range nonlinearity on star graph
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星图上长程非线性薛定谔方程的驻波散射失效
DOI：
10.1007/s00028-020-00579-w
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发表时间：
2020
影响因子：
1.4
通讯作者：
Mizutani Haruya
中科院分区：
文献类型：
--
作者：
Aoki Kazuki;Inui Takahisa;Mizutani Haruya
考虑星星图上具有幂型长程非线性项的薛定谔方程。在一般的边界条件下，包括Kirchhoff，Dirichlet，或边界条件，我们证明了非平凡的整体解不会散射到驻波。我们的证明基于Murphy和Nakanishi的论证（Failure of scattering to solid waves for long-range nonlinear Schrödinger equations），他们在欧氏空间中处理了具有一般势的长程非线性薛定谔方程，以考虑一般边界条件。
We consider the Schrödinger equation with power type long-range nonlinearity on star graph. Under a general boundary condition at the vertex, including Kirchhoff, Dirichlet,, orboundary condition, we show that the non-trivial global solution does not scatter to standing waves. Our proof is based on the argument by Murphy and Nakanishi (Failure of scattering to solitary waves for long-range nonlinear Schrödinger equations), who treated the long-range nonlinear Schrödinger equation with a general potential in the Euclidean space, in order to consider general boundary conditions.