Invariant solutions to the Khokhlov-Zabolotskaya singular manifold equation and their application

We find the Lie algebra of point symmetries for the singular manifold equation associated with the Khokhlov-Zabolotskaya equation (KhZ), classify one-dimensional subalgebras of this algebra, and find corresponding invariant solutions. Then we use the Bäcklund transformation between the singular manifold equation and KhZ to find new exact solutions to the last equation.