Nonlinear wave equations for low-frequency acoustic gravity waves

It is shown that low-frequency acoustic gravity waves propagating parallel to the earth's surface satisfy the Korteweg-De Vries equation or the Kadomtsev-Petviashvili equation and have a discrete spectrum of group velocities. The atmosphere is considered to be incompressible, homogeneous in composition and isothermal and the gravitational acceleration depends upon the height. The hydrostatic approximation is used and adapted in such a way that dispersion is not neglected. The nonlinear wave equations are obtained using the reductive perturbation technique. Finally, changes for a compressible atmosphere are discussed. -Author