  In this paper, two new classes of perfect nonlinear functions over
$\mathbb{F}_{p^{2m}}$ are proposed, where $p$ is an odd prime. Furthermore, we
investigate the nucleus of the corresponding semifields of these functions and
show that the semifields are not isotopic to all the known semifields.
Particularly, the new perfect nonlinear functions are CCZ-inequivalent to other
classes in general.
