  We study here the Zakharov-Kuznetsov equation in dimension $2$ and $3$ and
the modified Zakharov-Kuznetsov equation in dimension $2$. Those equations
admit solitons, characterized by their velocity and their shift. Given the
parameters of $K$ solitons $R^k$ (with distinct velocities), we prove the
existence and uniqueness of a multi-soliton $u$ such that $\left\| u-
\sum_{k=1}^K R^k \right\|_{H^1}\rightarrow 0 $ as $t \rightarrow +\infty$. The
convergence takes place in $H^s$ with an exponential rate for all $s\geq 0$.
The construction is made by successive approximations of the multi-soliton. We
use classical arguments to control of $H^1$-norms of the errors (inspired by
Martel [21]), and introduce a new ingredient for the control of the $H^s$-norm
in dimension $d \geq2$, by a technique close to monotonicity.
