  We investigate a hydrodynamic equation system which - with some approximation
- is capable to describe the tsunami propagation in the open ocean with the
time-dependent self-similar Ansatz. We found analytic solutions how the wave
height and velocity behave in time and space for constant and linear seabed
functions. First we study waves on open water, where the seabed can be
considered relatively constant, sufficiently far from the shore. In the second
part of the study we also consider a seabed which is oblique. Finally, we apply
the most common traveling wave Ansatz and present almost trivial solutions as
well.
