  The KP equation is a nonlinear dispersive wave equation which provides an
excellent model for resonant interactions of shallow-water waves. It is well
known that regular soliton solutions of the KP equation may be constructed from
points in the totally nonnegative Grassmannian Gr$(N,M)_{\geq 0}$. Kodama and
Williams studied the asymptotic patterns (tropical limit) of KP solitons,
called soliton graphs, and showed that they correspond to Postnikov's
Le-diagrams. In this paper, we consider soliton graphs for the KP hierarchy, a
family of commuting flows which are compatible with the KP equation. For the
positive Grassmannian Gr$(2,M)_{>0}$, Kodama and Williams showed that soliton
graphs are in bijection with triangulations of the $M$-gon. We extend this
result to Gr$(N,M)_{>0}$ when $N=3$ and $M=6,7$ and $8$. In each case, we show
that soliton graphs are in bijection with Postnikov's plabic graphs, which
generalize Le-diagrams.
