  The Generalized Minimal Massive Gravity (GMMG) theory is realized by adding
the CS deformation term, the higher derivative deformation term, and an extra
term to pure Einstein gravity with a negative cosmological constant. In the
present paper we obtain exact solutions to the GMMG field equations in the
non-linear regime of the model. GMMG model about $AdS_3$ space is conjectured
to be dual to a 2-dimensional CFT. We study the theory in critical points
corresponding to the central charges $c_-=0$ or $c_+=0$, in the non-linear
regime. We show that $AdS_3$ wave solutions are present, and have logarithmic
form in critical points. Then we study the $AdS_3$ non-linear deformation
solution. Furthermore we obtain logarithmic deformation of extremal BTZ black
hole. After that using Abbott-Deser-Tekin method we calculate the energy and
angular momentum of these types of black hole solutions.
