  We consider the Cauchy problem for the generalized Zakharov-Kuznetsov-Burgers
equation in 2D. This is one of the nonlinear dispersive-dissipative equations,
which has a spatial anisotropic dissipative term $-\mu u_{xx}$. In this paper,
we prove that the solution to this problem decays at the rate of
$t^{-\frac{3}{4}}$ in the $L^{\infty}$-sense, provided that the initial data
$u_{0}(x, y)$ satisfies $u_{0}\in L^{1}(\mathbb{R}^{2})$ and some appropriate
regularity assumptions. Moreover, we investigate the more detailed large time
behavior and obtain a lower bound of the $L^{\infty}$-norm of the solution. As
a result, we prove that the given decay rate $t^{-\frac{3}{4}}$ of the solution
to be optimal. Furthermore, combining the techniques used for the parabolic
equations and for the Schr$\ddot{\mathrm{o}}$dinger equation, we derive the
explicit asymptotic profile for the solution.
