Mathematics of nonlinear acoustics: analysis, numerics and applicatio...

Nonlinear imaging techniques can significantly enhance the image quality and are therefore of great interest in medical but also industrial areas. This talk covers the basic concepts from nonlinear acoustics to nonlinear wave equations. First, we look at nonlinear wave propagation and then the modeling of it. Therefore, an overview of some important nonlinear acoustic wave equations is presented. The focus is on the Westervelt and KZK equation, two second order nonlinear wave equations which are related via a paraxial approximation that changes the equation significantly. These equations contain a nonlinearity parameter which is sensitive to differences in the tissue properties and therefore can be used for imaging purposes. So, the reconstruction of this parameter is one way for achieving an image.