Abstract The Zakharov-Kuznetsov equation has been derived by a number of authors in the context of a fluid description as well as a kinetic description in a nonmagnetized plasma. We propose, in this short paper, to discuss the derivation of the equation governing the evolution of ion acoustic waves in a magnetized plasma using kinetic theory. This allows us to introduce Landau damping more specifically, as well as other purely nonlinear kinetic effects. We first investigate the effects of Landau damping on the conservation laws, and therefore on the solitary solution known to exist in the fluid regime. We also derive a conservation law very much like the one-dimensional case.