In this paper, we consider the quadratic nonlinear Schrödinger system in three space dimensions. Our aim is to obtain sharp scattering criteria. Because of the mass-subcritical nature, it is difficult to do so in terms of conserved quantities. The corresponding single equation is studied by the second author and a sharp scattering criterion is established by introducing a distance from a trivial scattering solution, the zero solution. By the structure of the nonlinearity we are dealing with, the system admits a scattering solution which is a pair of the zero function and a linear Schrödinger flow. Taking this fact into account, we introduce a new optimizing quantity and give a sharp scattering criterion in terms of it.

中文翻译：

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亚次临界非线性Schrödinger系统的尖锐散射阈值水平

在本文中，我们考虑了三个空间维度上的二次非线性Schrödinger系统。我们的目标是获得清晰的散射标准。由于具有亚临界性质，因此很难做到守恒。第二作者研究了相应的单个方程，并通过引入与平凡散射解（零解）的距离来建立尖锐的散射准则。通过我们要处理的非线性结构，系统允许一个零解和线性薛定ding流对的散射解。考虑到这一事实，我们引入了一个新的优化量，并给出了一个明确的散射标准。