Convolutional Neural Networks (CNNs) have recently been introduced for addressing copy-move forgery detection (CMFD). However, current CMFD CNN-based approaches have insufficient performance commitment regarding the localization of the positive class. In this paper, this issue is explored by considering both linear and nonlinear interactions between pixels. A nonlinear Inception module based on second-order Volterra kernels is proposed, in order to ameliorate the results of a state-of-the-art CMFD architecture. The outcome of this work shows that a combination of linear and nonlinear convolution kernels can make the input foreground and background pixels more separable. The proposed approach is evaluated on CASIA and CoMoFoD, two publicly available CMFD datasets, and results to an improved positive class localization performance. Moreover, the findings of the proposed method imply that the nonlinear Inception module stimulates immense robustness against miscellaneous post processing attacks.