We use our vector Maxwell’s nonlinear eigenmode solver to study the stationary solutions in 2D cross-section plasmonic slot waveguides with isotropic Kerr nonlinear codes and anisotropic Kerr nonlinear cores. First, for the isotropic case, we demonstrate that, even in the low-power regime, 1D stud- ies may not provide accurate and meaningful results compared to 2D ones. Second, we study, including at high powers, the link between the nonlinear parameter γ nl and the change of the nonlinear propagation constant Δβ. Third, we demon- strate that our approach is also valid for anisotropic wave- guides, and we show how to improve by, a factor of 2, the figure of merit of nonlinear plasmonic slot waveguides using realistic materials.