AI 中文总结
本文研究二次非线性薛定谔方程三分量系统的柯西问题，证明带双频率参数的孤波基态存在性、基态存在的频率参数条件依赖系统共振结构，改进两类初值的整体适定性，并证明小速度参数下基态集的轨道稳定性。
AI 中文摘要
本文研究了一个具有二次非线性的三分量非线性薛定谔方程组的柯西问题。首先，我们证明了带双频率参数的孤波解形式的基态的存在性。接着，我们表明基态存在所需的频率参数条件取决于该系统的共振结构。然后，我们给出了两个关于整体解的结果：第一个是对低于基态阈值的初值的整体适定性的改进；第二个是对振荡初值的整体适定性的改进。我们还证明了带小速度参数的基态集的轨道稳定性。
英文摘要
In the present paper, we consider the Cauchy problem of a system of three nonlinear Schrödinger equations with quadratic nonlinearity. We first prove the existence of ground states in the form of solitary wave solutions with two frequency parameters. We then show that the conditions on the frequency parameters for the existence of ground states depend on the resonance structure of the system. Next, we give the two results for global solutions. The first is an improvement of global well-posedness for initial data below the ground state threshold. The second is an improvement of global well-posedness for oscillating initial data. We also prove the orbital stability of the ground state sets with small speed parameter.
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