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In this article, we prove that small localized data yield solutions toKawahara type equation which have linear dispersive decay on a finite time. Weuse the similar method used to derive the dispersive decay bound of thesolutions to the KdV equation, with some steps being simpler. This result isexpected to be the first result of the small data global bounds of thefifth-order dispersive equations with quadratic nonlinearity.

Dispersive Decay Bound of Small Data Solutions to Kawahara Equation in a Finite Time Scale