  In this work, we study the random series expansion of a multidimensional KdV
type equation with a diffusion term, the so-called Zakharov-Kuznetsov (ZK)
equation. We impose random initial data and periodic boundary condition with
period $L$ on this equation. Using the random series expansion, we derive the
$3$-wave kinetic equation on the inertial range for $t\lesssim
L^{-\varepsilon}T_{\text{kin}}$. Our result reaches kinetic time scale up to
$\varepsilon$ loss.
