  We present a detailed numerical study of solutions to the (generalized)
Zakharov-Kuznetsov equation in two spatial dimensions with various power
nonlinearities. In the $L^{2}$-subcritical case, numerical evidence is
presented for the stability of solitons and the soliton resolution for generic
initial data. In the $L^2$-critical and supercritical cases, solitons appear to
be unstable against both dispersion and blow-up. It is conjectured that blow-up
happens in finite time and that blow-up solutions have some resemblance of
being self-similar, i.e., the blow-up core forms a rightward moving
self-similar type rescaled profile with the blow-up happening at infinity in
the critical case and at a finite location in the supercritical case. In the
$L^{2}$-critical case, the blow-up appears to be similar to the one in the
$L^{2}$-critical generalized Korteweg-de Vries equation with the profile being
a dynamically rescaled soliton.
