Oscillations of a rotating stratified fluid with its free surface excited by moving sources

Propagation of small perturbations in a weakly stratified inviscid fluid rotating at a constant angular velocity in the lower half-space is studied. The source of excitation is a plane wave traveling on the free surface of the fluid. An explicit analytical solution to the problem is constructed. Existence and uniqueness theorems are proved. The long-time wave pattern in the fluid is analyzed.