  The study of noncommutative solitons is greatly facilitated if the field
equations are integrable, i.e. result from a linear system. For the example of
a modified but integrable U(n) sigma model in 2+1 dimensions we employ the
dressing method to construct explicit multi-soliton configurations on
noncommutative R^{2,1}. These solutions, abelian and nonabelian, feature exact
time-dependence for any value of the noncommutativity parameter theta and
describe various lumps of finite energy in relative motion. We discuss their
scattering properties and prove asymptotic factorization for large times.
