  The Seiberg-Witten limit of fermionic N=2 string theory with nonvanishing
B-field is governed by noncommutative self-dual Yang-Mills theory (ncSDYM) in
2+2 dimensions. Conversely, the self-duality equations are contained in the
equation of motion of N=2 string field theory in a B-field background.
Therefore finding solutions to noncommutative self-dual Yang-Mills theory on
R^{2,2} might help to improve our understanding of nonperturbative properties
of string (field) theory. In this paper, we construct nonlinear soliton-like
and multi-plane wave solutions of the ncSDYM equations corresponding to certain
D-brane configurations by employing a solution generating technique, an
extension of the so-called dressing approach. The underlying Lax pair is
discussed in two different gauges, the unitary and the hermitean gauge. Several
examples and applications for both situations are considered, including abelian
solutions constructed from GMS-like projectors, noncommutative U(2)
soliton-like configurations and interacting plane waves. We display a
correspondence to earlier work on string field theory and argue that the
solutions found here can serve as a guideline in the search for nonperturbative
solutions of nonpolynomial string field theory.
