The paper deals with the construction of exact singular solutions of the Kuznetsov equation, better known as the Khokhlov-Zabolotskaya-Kuznetsov equation (KZK). This equation is a third-order partial differential equation and describes the propagation of a bounded sound beam in a nonlinear medium with dissipation. To construct exact solutions, the methods of the modern theory of symmetries of differential equations and the theory of singular solutions are used. Also, in this paper, some solutions are visualized, in particular, a solution that corresponds to the effect of focusing the sound beam.
02.20.Qs General properties, structure, and representation of Lie groups
02.40.Xx Singularity theory
$^1$Institute of Control Sciences RAS
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