Moving boundary shallow water flow above parabolic bottom topography

Exact solutions of the two dimensional nonlinear shallow water wave equations for flow involving linear bottom friction and with no forcing are found for flow above parabolic bottom topography. These solutions also involve moving shorelines. The motion decays over time. In the solution of the three simultaneous nonlinear partial differential shallow water wave equations it is assumed that the velocity is a function of time only and along one axis. This assumption reduces the three simultaneous nonlinear partial differential equations to two simultaneous linear ordinary differential equations . The solutions found are useful for testing numerical solutions of the nonlinear shallow water wave equations which include bottom friction and whose flow involves moving shorelines.