  We investigate the conductivity of charge carriers confined to a
two-dimensional system with the non-parabolic dispersion $k^N$ with $N$ being
an arbitrary natural number. A delta-shaped scattering potential is assumed as
the major source of disorder. We employ the exact solution of the
Lippmann-Schwinger equation to derive an analytical Boltzmann conductivity
formula valid for an arbitrary scattering potential strength. The range of
applicability of our analytical results is assessed by a numerical study based
on the finite size Kubo formula. We find that for any $N>1$, the conductivity
demonstrates a linear dependence on the carrier concentration in the limit of a
strong scattering potential strength. This finding agrees with the conductivity
measurements performed recently on chirally stacked multilayer graphene where
the lowest two bands are non-parabolic and the adsorbed hydrocarbons might act
as strong short-range scatterers.
