F (U,V) = 0

G (U,V) = 0

Phase portrait analysis on the basis of the geometric theory of ordinary differential equations was used to study the travelling wave solution properties. The result indicates that there are no solitary waves in the nonlinear system.

In order to obtain the dispersive relationship of the finite amplitude inertia-gravity wave, Taylor expansion was used in the above system at the equilibrium point (0,0). Using the K-B average method in the expansion yield, the dispersive relationship can be written as (For the equations please see the PDF file.) (Rossby number for inertia-gravity wave). Thus, the dispersive relationship includes Rossby number and the circular frequency σ increases with ε.