A nonlinear Liouville property for the generalized Kawahara equation

In this paper, by applying the method of Martel and Merle [9], we prove that if the global solution of the generalized Kawahara equation (gKW) is close to the soliton (constructed by Kabakouala and Molinet [4]) at initial time in the energy space, moreover if this solution is uniformly localized, then it is identically equal to a soliton all time. © 2019 Elsevier Inc.