Instantons and scattering in N=4 SYM in 4D

: We study classical solutions (ic–instantons) in N = 4 SYM in 4D which, in the strong coupling limit, correspond to complex two–dimensional manifolds. Asymptotically in time the latter have boundaries represented by compact real three–manifolds. Therefore they lend themselves to an interpretation in terms of 3–brane scattering. We suggest that these solutions may represent scattering of D3–branes of type IIB theory in 10D. In particular we show that the world–volume theory on complex two–dimensional manifolds is the correct one for D3–branes.