  Let $p\in\mathbb Z^n$ be a primitive vector and $\Psi:\mathbb Z^n\to \mathbb
Z, z\to \min(p\cdot z, 0)$. The theory of {\it husking} allows us to prove that
there exists a pointwise minimal function among all integer-valued
superharmonic functions equal to $\Psi$ "at infinity".
  We apply this result to sandpile models on $\mathbb Z^n$. We prove existence
of so-called {\it solitons} in a sandpile model, discovered in 2-dim setting by
S. Caracciolo, G. Paoletti, and A. Sportiello and studied by the author and M.
Shkolnikov in previous papers. We prove that, similarly to 2-dim case, sandpile
states, defined using our husking procedure, move changeless when we apply the
sandpile wave operator (that is why we call them solitons).
  We prove an analogous result for each lattice polytope $A$ without lattice
points except its vertices. Namely, for each function $$\Psi:\mathbb Z^n\to
\mathbb Z, z\to \min_{p\in A\cap \mathbb Z^n}(p\cdot z+c_p), c_p\in \mathbb Z$$
there exists a pointwise minimal function among all integer-valued
superharmonic functions coinciding with $\Psi$ "at infinity". The laplacian of
the latter function corresponds to what we observe when solitons, corresponding
to the edges of $A$, intersect (see Figure~1).
