  By integrating the Seiberg-Witten differential equation in a special path, we
write ordinary gauge fields in terms of their non-commutative counterparts up
to three non-commutative gauge fields. We then use this change of variables to
write ordinary abelian Dirac-Born-Infeld action in terms of non-commutative
fields. The resulting action is then compared with various low energy contact
terms of world-sheet perturbative string scattering amplitudes from
non-commutative D$p$-brane. We find completely agreement between the field
theory and string theory results. Hence, it shows that perturbative string
theory knows the solution of the Seiberg-Witten differential equation.
