Abstract
Solitary waves in a compressible atmosphere of finite or infinite height with arbitrary wind and density profiles are studied. Explicit expressions for the critical speed and the first-order solution of the internal solitary waves are obtained by a perturbation scheme applied to the nonlinear equations and are expressed in terms of simple integrals of velocity and density profiles of the atmosphere in the state of equilibrium. The slope of the density profile at the bottom surface plays an important role in determining the signature of the wave, and solitary waves do not appear when the parameters involved in the solitary wave solution assume certain critical values. The results obtained cover many of the existing solitary wave solutions as special cases.
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