Self-influence of the collapsing internal gravity wave in the inhomogeneous atmosphere

Nonlinear equations for internal gravity waves in the atmosphere in the presence of the inhomogeneous wind velocity leading to the wave collapse are derived. In frameworks of the WKB-solutions justified right up to the collapse point the cubic nonlinearity at the fundamental wave frequency is found. It is shown that the nonlinearity results in displacement of the collapse before the linear collapse point. A comparison between a role of the nonlinearity and viscosity is carried out.