In the paper, we establish the local well-posedness of the Schödinger-Boussinesq system on the half line with data of low regularity. The proof is based on the explicit solution formula of the linear boundary problem and the restricted norm method. Besides, we prove that the nonlinearity is smoother than the initial data. Our result match the known result on the full line in [9].

中文翻译：

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Schrödinger-Boussinesq系统初边值问题的适定性

在本文中，我们用低规则性数据在半线上建立了Schödinger-Boussinesq系统的局部适定性。证明是基于线性边界问题的显式求解公式和约束范数方法。此外，我们证明了非线性比初始数据更平滑。我们的结果与[9]中实线上的已知结果相匹配。