  We establish existence and stabilty results for solitons in noncommutative
scalar field theories in even space dimension $2d$. In particular, for any
finite rank spectral projection $P$ of the number operator ${\mathcal N}$ of
the $d$-dimensional harmonic oscillator and sufficiently large noncommutativity
parameter $\theta$ we prove the existence of a rotationally invariant soliton
which depends smoothly on $\theta$ and converges to a multiple of $P$ as
$\theta\to\infty$.
  In the two-dimensional case we prove that these solitons are stable at large
$\theta$, if $P=P_N$, where $P_N$ projects onto the space spanned by the $N+1$
lowest eigenstates of ${\mathcal N}$, and otherwise they are unstable. We also
discuss the generalisation of the stability results to higher dimensions. In
particular, we prove stability of the soliton corresponding to $P=P_0$ for all
$\theta$ in its domain of existence.
  Finally, for arbitrary $d$ and small values of $\theta$, we prove without
assuming rotational invariance that there do not exist any solitons depending
smoothly on $\theta$.
