Analytical solutions for diffraction problem of nonlinear acoustic wave beam in the stratified atmosphere

The nonlinear wave equation and modified Khokhlov-Zabolotskaya type equation for high intensive acoustics wave beams propagating in stratified atmosphere with inhomogeneous of sound speed is set up. Some approaches to find analytical solutions of this equation are developed. The geometrical acoustics approximation and modified Raley integral for this problem is suggested. The asymptotical procedure is developed for describing of wave profile near the axis of wave beam. This method allows to take into account phase distortion due to diffraction and nonlinear effects and improve the nonlinear geometrical acoustics solution.