Using a general barotropic potential vorticity model that includes the time rate of change of the topographic vorticity, solitonlike solutions over variable bottom topography are obtained. To lowest order, the solution is the classic topographic wave. The solvability condition for the next order yields solitonlike solutions. The scaling regime for these solutions applies to topography steeper than that used in quasi-geostrophic potential vorticity models of solitons. ¿1991 American Geophysical Union