  Given a point A in the real Grassmannian, it is well-known that one can
construct a soliton solution u_A(x,y,t) to the KP equation. The contour plot of
such a solution provides a tropical approximation to the solution when the
variables x, y, and t are considered on a large scale and the time t is fixed.
In this paper we use several decompositions of the Grassmannian in order to
gain an understanding of the contour plots of the corresponding soliton
solutions. First we use the positroid stratification of the real Grassmannian
in order to characterize the unbounded line-solitons in the contour plots at
y>>0 and y<<0. Next we introduce a refinement of the positroid stratification
-- the Deodhar decomposition of the Grassmannian -- which is defined to be the
projection of Deodhar's decomposition of the complete flag variety. We index
the components of the Deodhar decomposition of the Grassmannian by certain
tableaux which we call Go-diagrams, and then use these Go-diagrams to
characterize the contour plots of solitons solutions when t<<0. Finally we use
these results to show that a soliton solution u_A(x,y,t) is regular for all
times t if and only if A comes from the totally non-negative part of the
Grassmannian.
