The extension of the nonlinear drift wave equation including the two-dimensional vector non-linearity by Lakhin et al. (1987, 1988) has found much interest in recent theoretical and experimental investigations. In this study the authors present periodical solutions alternatively to the localized soliton solutions in the one-dimensional limits and the localized vortex solutions in two-dimensions. They therefore extend a perturbation scheme, which has recently been employed to a (quasi-) one-dimensional limit (Kauschke and Schluter, 1991), to the two-dimensional situation.