  The amorphous solids can be theoretically modeled by anharmonic disordered
lattices. However, most of theoretical studies on thermal conductivity in
anharmonic disordered lattices only focus on the potentials of hard-type (HT)
anharmonicity. Here we study the thermal conductivity $\kappa$ of
one-dimensional (1D) disordered lattices with both hard- and soft-type (ST)
anharmonic on-site potentials. It is found, via both direct molecular dynamic
simulations and theoretical method, that the anharmonicity dependence of
$\kappa$ in the HT model is nonmonotonous, while in the ST model is
monotonously increased. This provides a new way to enhance thermal conductivity
in disordered systems. Furthermore, $\kappa$ of the HT model is consistent with
the prediction of the quasi-harmonic Green-Kubo (QHGK) method in a wide range
of anharmonicity, while for the ST model, the numerical results seem largely
deviated from the theoretical predictions as the anharmonicity becomes soft.
This new and peculiar feature of the ST model may root in the fact that only
delocalization effect exists, different from the competing roles that both
delocalization and localization play in the counterpart HT model.
