  New exact solutions, nonstationary and stationary, of Veselov-Novikov (VN)
equation in the forms of linear superpositions of arbitrary number of exact
special solutions $u^{(n)}$, $n=1,...,N$ are constructed via
$\bar\partial$-dressing method in such a way that the sums $u= u^{(k_1)}+...+
u^{(k_m)}$, $1\leqslant k_1<k_2<...<k_m\leqslant N$ of arbitrary subsets of
these solutions are also exact solutions of VN equation. The presented linear
superpositions include as superpositions of special line solitons with zero
asymptotic values at infinity and also superpositions of special plane wave
type singular periodic solutions. By construction these exact solutions
represent also new exact transparent potentials of 2D stationary
Schr\"{o}dinger equation and can serve as model potentials for electrons in
planar structures of modern electronics.
