  Inspired by large applications of topological defects in describing different
phenomena in physics, and considering the importance of three dimensional
solutions in AdS/CFT correspondence, in this paper we obtain magnetic anti-de
Sitter solutions of nonlinear electromagnetic fields. We take into account
three classes of nonlinear electrodynamic models; first two classes are the
well-known BornInfeld like models including logarithmic and exponential forms
and third class is known as the power Maxwell invariant nonlinear
electrodynamics. We investigate the effects of these nonlinear sources on three
dimensional magnetic solutions. We show that these asymptotical AdS solutions
do not have any curvature singularity and horizon. We also generalize the
static metric to the case of rotating solutions and find that the value of the
electric charge depends on the rotation parameter. Finally, we consider the
quadratic Maxwell invariant as a correction of Maxwell theory and in other
words, we investigate the effects of nonlinearity as a correction. We study the
behavior of the deficit angle in presence of these theories of nonlinearity and
compare them with each other. We also show that some cases with negative
deficit angle exists which are representing objects with different geometrical
structure. We also show that in case of the static only magnetic field exists
whereas by boosting the metric to rotating one, electric field appear too.
