The nonlinear evolution of tearing modes in an inhomogeneous plasma is a numerically challenging problem involving scale lengths ranging from less than the ion Larmor radius to the macroscopic dimensions, and time scales ranging from the electron transit time to the skin time. We use methods exploiting the scale-separation to reduce the problem to a 1.5-dimensional system of nonlinear equations. We then solve these equations numerically as well as analytically in relevant asymptotic regimes. Our solutions show that the density gradient is maintained within the separatrix even when the island width exceeds the Larmor radius, and that the islands propagate at a velocity close to the drift velocity for the electrons. We will discuss the conditions necessary for the success of our method and its implications for numerical techniques for dealing with anisotropic heat conduction.
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