On the unique continuation property of solutions of the three-dimensional Zakharov-Kuznetsov equation

Abstract

We prove that if the difference of two sufficiently smooth solutions of the three-dimensional Zakharov-Kuznetsov equation $${\partial }_{t}u+{\partial }_x△u+u{\partial }_{x}u=0\text{,}(x,y,z)\in {\mathbb{R}}^3,t\in [0,1],$$ decays as $e^{-a(x^2+y^2+z^2{)}^{3/4}}$ at two different times, for some $a>0$ large enough, then both solutions coincide.