In this paper we investigate ghost dark energy model in the presence of non-linear interaction between dark energy and dark matter .
We also extend the analysis to the so called generalized ghost dark energy ( GGDE ) which \rho _ { D } = \alpha H + \beta H ^ { 2 } .
The model contains three free parameters as \Omega _ { D } , \zeta ( = \frac { 8 \pi G \beta } { 3 } ) and b ^ { 2 } ( the coupling coefficient of interactions ) .
We propose three kinds of non-linear interaction terms and discuss the behavior of equation of state , deceleration and dark energy density parameters of the model .
We also find the squared sound speed and search for signs of stability of the model .
To compare the interacting GGDE model with observational data sets , we use more recent observational outcomes , namely SNIa from JLA catalog , Hubble parameter , baryonic acoustic oscillation and the most relevant CMB parameters including , the position of acoustic peaks , shift parameters and redshift to recombination .
For GGDE with the first non-linear interaction , the joint analysis indicates that \Omega _ { D } = 0.7192 \pm 0.0062 , b ^ { 2 } = 0.146 ^ { +0.030 } _ { -0.026 } and \zeta = 0.104 \pm 0.047 at 1 optimal variance error .
For the second interaction , the best fit values at 1 \sigma confidence are \Omega _ { D } = 0.72091 \pm 0.0065 , b ^ { 2 } = 0.0395 \pm 0.0080 and \zeta \leq 0.0173 .
According to combination of all observational data sets considered in this paper the best fit values for third non-linearly interacting model are \Omega _ { D } = 0.7287 \pm 0.0062 , b ^ { 2 } = 0.0109 \pm 0.0023 and \zeta \leq 0.00764 at 1 \sigma confidence interval .
Finally we found that the presence of interaction is compatible in mentioned models via current observational datasets .