### Chirkunov Y.A. Belmetsev N.

## Submodels of Khohlov-Zabolotskaya-Kuznetsov model of nonlinear hydroacoustics with dissipation

### Reporter: Chirkunov Y.A.

We study three-dimensional Khokhlov-Zabolotskaya-Kuznetsov (KZK) model of the nonlinear hydroacoustics with dissipation [1] . This model is described by third order quasilinear partial differential equation of the (KZK). We obtained that the (KZK) equation admits an infinite Lie group of the transformations, depending on the three arbitrary functions. We studied the submodels of rank 0 and 1, described by the invariant solutions of the (KZK) equation. These solutions are found either explicitly, or their search is reduced to the solution of the nonlinear integro-differential equations. For example, we obtained the solutions that we called by "Ultrasonic knife" and "Ultrasonic destroyer". For the submodel "Ultrasonic knife" at each fixed moment of the time in the field of the existence of the solution near a some plane the pressure increases indefinitely and becomes infinite on this plane. The submodel "Ultrasonic destroyer" contains a countable number of "Ultrasonic knives". With a help of the invariant solutions we researched a propagation of the intensive acoustic waves (one-dimensional, axisymmetric and planar) for which the acoustic pressure, speed and acceleration of its change, or the acoustic pressure, speed and acceleration of its change in the radial direction, or the acoustic pressure, speed and acceleration of its change in the direction of one of the axes are specified at the initial moment of the time at a fixed point. Under the certain additional conditions, we established the existence and the uniqueness of the solutions of boundary value problems, describing these wave processes.

The reported study was funded by RFBR according to the research project № 16-01-00446 а and by Novosibirsk State University of Architecture and Civil Engineering.

The reported study was funded by RFBR according to the research project № 16-01-00446 а and by Novosibirsk State University of Architecture and Civil Engineering.

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