Abstract
A simple incompressible non-hydrostatic Boussinesq equation with the influence of air–sea interaction is applied to investigate the non-linear internal gravity waves in the atmosphere. By the phase plane analysis method and power series expansion method, we derived the KdV equation and Gardner equation. We obtain various periodic structures for the internal gravity waves with the help of direct integration method and the transformation method based on the projective Riccati equation analysis. It is shown that the air–sea interaction is very important for these periodic structures of the waves.
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