Asymptotic stability of a finite sum of solitary waves for the Zakharov-Kuznetsov equation

Abstract: We prove the asymptotic stability of a finite sum of well-ordered solitary waves for the Zakharov-Kuznetsov equation in dimensions two and three. Moreover, we derive a qualitative version of the orbital stability result which turns out to be useful for the study of the collision of two solitary waves. The proof extends the ideas of Martel, Merle and Tsai for the sub-critical gKdV equation in dimension one to the higher-dimensional case. It relies on monotonicity properties on oblique half-spaces and rigidity properties around one solitary wave introduced by C^ote, Mu~noz, Pilod and Simpson in dimension two, and by Farah, Holmer, Roudenko and Yang in dimension three.