  Early results concerning the linear stability of the solitons in equation of
the KDV-type \cite{KUZNETSOV1984314} are generalized to solitons describing by
the ZK-type equation. The linear stability criterion for ground solitons in the
Vakhitov-Kolokolov form is derived for such equations with arbitrary
nonlinearity. For the power nonlinearity the instability criterion coincides
with the condition of the Hamiltonian unboundedness from below. The latter
represents the main feature for appearance of collapse in such systems.
