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

Abstract

In this paper, we present the first result concerning the orbital stability of periodic traveling waves for the modified Kawahara equation. Our method is based on the Fourier expansion of the periodic wave in order to know the behaviour of the nonpositive spectrum of the associated linearized operator around the periodic wave combined with a recent development which significantly simplifies the obtaining of orbital stability results.

arXiv comment8 pages. arXiv admin note: text overlap with arXiv:1902.04402 To appear in Applicable Analysis