Using a new two-dimensional nonlinear finite element model, we investigate the interaction of dispersive shear Alfv¿n wave (SAW) field line resonances (FLRs) and ion acoustic waves in Earth's magnetosphere. We solve the full set of nonlinear reduced MHD equations self-consistently in arbitrary geometries. Initially, a Cartesian box model is used to demonstrate the reliability of our numerical solution in determining the linear and nonlinear evolution of FLRs. Then the full reduced MHD equations with the effects of electron inertia, ion Larmor radius correction, and electron thermal pressure are solved in dipolar and stretched magnetic topologies. We show that time-dependent dispersion and density steepening lead to localization of a highly structured FLR within an ionospheric (equatorial) density cavity (bump). When nonlinear effects are accounted for, we find that FLRs preferentially form in regions of low wave dispersion. Field line stretching and ponderomotive density redistribution lead to a significant reduction in FLR eigenfrequencies, bringing them into the range of observations. Nonlinear effects also cause a rapid acceleration of the timescale over which small perpendicular spatial scales appear. In our model, it is shown that density perturbations can be comparable to the equilibrium background density.