Orbital Stability of Periodic Waves for the Log-KdV Equation

Fabio Natali, Ademir Pastor

Published 2014-08-07, updated 2014-09-12Version 2

In this paper we evidence the orbital stability of positive 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 spectral properties of the associated linearized operator, we can apply the abstract theory in \cite{grillakis1} to deduce the orbital stability in the periodic setting.