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Here $\\beta>0(<0)$ corresponds to the positive (negative) dispersion of the media, respectively. P. Isaza and J. Mej\\'{\\i}a (J. Diff. Eqns. 230(2006), 601-681; Nonli. Anal. 70(2009), 2306-2316), K. Tsugawa (J. Diff. Eqns. 247(2009), 3163-3180) proved that the problem is locally well-posed in $H^s(\\R)$ when $s>-3/4$ and ill-posed when $s<-3/4$. 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