Shallow water theory and solution of the problem on the atmospheric motion around a celestial body

Free boundary problem for a fluid circulating around a solid circle is considered as a two dimensional mathematical model for longitudinal motion of an atmosphere around a celestial body. Two different systems of Shallow Water Equations for the problem are derived in the non-stationary case. The solutions to the problem are obtained in an explicit form and it is shown that the solutions are progressive solitary waves describing periodic atmospheric motions. A detailed analysis of the solutions is given in this paper.