we study an initial-boundary-value problem for the “good” Boussinesq equation on the half line \documentclass[12pt]{minimal}
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\left\{ \begin{gathered}
\partial _t^2 u - \partial _x^2 u + \partial _x^4 u + \partial _x^2 u^2 = 0, t > 0, x > 0, \hfill \\
u\left( {0,t} \right) = h_1 \left( t \right), \partial _x^2 u\left( {0,t} \right) = \partial _t h_2 \left( t \right), \hfill \\
u\left( {x,0} \right) = f\left( x \right), \partial _t u\left( {x,0} \right) = \partial _x h\left( x \right) \hfill \\
\end{gathered} \right.
$$\end{document}. The existence and uniqueness of low reguality solution to the initial-boundary-value problem is proved when the initial-boundary data (f, h, h1, h2) belong to the product space \documentclass[12pt]{minimal}
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H^s \left( {\mathbb{R}^ + } \right) \times H^{s - 1} \left( {\mathbb{R}^ + } \right) \times H^{\tfrac{s}
{2} + \tfrac{1}
{4}} \left( {\mathbb{R}^ + } \right) \times H^{\tfrac{s}
{2} + \tfrac{1}
{4}} \left( {\mathbb{R}^ + } \right)
$$\end{document} with \documentclass[12pt]{minimal}
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0 \leqslant s \leqslant \tfrac{1}
{2}
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. The analyticity of the solution mapping between the initial-boundary-data and the solution space is also considered.
