Abstract: nonlinear equation that describes a process of acoustic waves propagation is considered. An inverse problem of recovering coefficient under nonlinearity depending from space variables is studied. It is supposed that the coefficient is a finite function and its support is contained in the ball BR. The unknown coefficient is related with certain physical parameters of a medium that play very important role in the medical diagnostics. For solving the inverse problem, a direct problem related to a running wave going in a homogeneous media from infinity in the direction of the unite vector ν is considered for the nonlinear acoustics equation. The parameter ν is variable and it can run the unite sphere of the three-dimensional space. At the moment of time t = 0 the wave reaches the boundary of the ball BR, then passes throughBR and registered at its boundary. An inverse problem of recovering the coefficient under nonlinearity is posed. It is assumed that the following information about the solution of the running plane wave is given: values of the derivative with respect to time of the sound pressure are known at moments arriving the wave to the boundary of the ball BR. It is shown that the inverse problem is reduced to the well studied problem of X-ray tomography. It allows to effectively reconstruct the desired coefficient.

Cite: Romanov V.G.
An inverse problem for a nonlinear acoustics equation
International conference “Days on Diffraction 2026" 01-05 Jun 2026