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In this paper, we investigate the orbital stability of periodic traveling waves for the Kawahara equation. We prove that the periodic traveling wave, under certain conditions, minimizes a convenient functional… Click to show full abstract
In this paper, we investigate the orbital stability of periodic traveling waves for the Kawahara equation. We prove that the periodic traveling wave, under certain conditions, minimizes a convenient functional by using an adaptation of the method developed by Grillakis et al. [J. Funct. Anal. 74, 160–197 (1987)]. The required spectral properties to ensure the orbital stability are obtained by knowing the positiveness of the Fourier transform of the associated periodic wave established by Angulo and Natali [SIAM J. Math. Anal. 40, 1123–1151 (2008)].
Journal Title: Journal of Mathematical Physics
Year Published: 2017
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