Orbital Stability of Periodic Waves for the Log-KdV Equation

Abstract: In this paper we establish the orbital stability of periodic waves related to the logarithmic Korteweg-de Vries equation. Our motivation is inspired in the recent work \cite{carles}, in which the authors established the well-posedness and the linear stability of Gaussian solitary waves. By using the approach put forward recently in \cite{natali1} to construct a smooth branch of periodic waves as well as to get the spectral properties of the associated linearized operator, we apply the abstract theories in \cite{grillakis1} and \cite{weinstein1} to deduce the orbital stability of the periodic traveling waves in the energy space.