  Let $k$ be a $p$-adic field and let $\mathbf{G}(k)$ be the $k$-points of a
connected reductive group, inner to split. The set of Aubert-Zelevinsky duals
of the constituents of a tempered L-packet form an Arthur packet for
$\mathbf{G}(k)$. In this paper, we give an alternative characterization of such
Arthur packets in terms of the wavefront set, proving in some instances a
conjecture of Jiang-Liu and Shahidi. Pursuing an analogy with real and complex
groups, we define some special unions of Arthur packets which we call
\emph{weak} Arthur packets and describe their constituents in terms of their
Langlands parameters.
