There has been some interest recently in the dynamics of buoyant low viscosity conduits in surrounding more viscous fluids, motivated by applications to geophysical phenomena. Most studies have been concerned with axisymmetric cylindrical conduits, and have shown that these conduits can support robust solitary waves. Here we develop the wave evolution equation for the analogous two-dimensional slab conduit, and show that this case also supports solitary waves, which are apparently stable and can effectively survive collisions.