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The main result shows that: for initial datum $u_{0}\\in H^{s}(\\mathbb{R})$ with $s>3/4,$ if the restriction of $u_{0}$ belongs to $H^{l}((x_{0}, \\infty))$ for some $l\\in \\mathbb{Z}^{+}$ and $x_{0}\\in \\mathbb{R},$ then the restriction of the corresponding solution $u(\\cdot, t)$ belongs to $H^{l}((\\alpha, \\infty))$ for any $\\alpha\\in \\mathbb{R}$ and any $t\\in(0, T)$. 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