Asymptotics of Shallow Water Equations on the Sphere

We consider the Shallow Water Equations on the sphere in the basin with nonuniform bottom. Using recently developed approach based on generalized Maslov canonical operator we construct quite explicit asymptotic formulas for the solutions to the Cauchy problem with spatially localized initial data. These solutions in particular describe propagation of tsunami waves in frame of so-called piston model. We discuss the following question: to what extent can the spherical property of the Earth influence the front and the profile (amplitude) of the wave generated by spatially localized momentary sources. We also discuss the problem concerning the influence of the Coriolis force into the solution.