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In this paper, we present the first result concerning the orbital stabilityof periodic traveling waves for the modified Kawahara equation. Our method isbased on the Fourier expansion of the periodic wave in order to know thebehaviour of the nonpositive spectrum of the associated linearized operatoraround the periodic wave combined with a recent development which significantlysimplifies the obtaining of orbital stability results.

On the Stability of Periodic Traveling Waves for the Modified Kawahara Equation