  We show that noncommutative electromagnetism and Dirac-Born-Infeld (DBI)
theory with scalar fields are SL(2,R) self-dual when noncommutativity is
light-like and we are in the slowly varying field approximation. This follows
from SL(2,R) self-duality of the commutative DBI Lagrangian and of its zero
slope limit that we study in detail.
  We study a symmetry of noncommutative static configurations that maps
space-noncommutativity into space-time (and light-like) noncommutativity.
SL(2,R) duality is thus extended to space-noncommutativity. Via Seiberg-Witten
map we study the nontrivial action of this symmetry on commutative DBI theory.
In particular space-time noncommutative BPS magnetic monopoles corresponds to
commutative BPS type magnetic monopoles with both electric and magnetic B-field
background. Energy, charge and tension of these configurations are computed and
found in agreement with that of a D1-string D3-brane system. We discuss the
dual string-brane configuration.
