Determining the nonlinearity in an acoustic wave equation

We consider an undetermined coefficient inverse problem for a nonlinear partial differential equation describing high-intensity ultrasound propagation as widely used in medical imaging and therapy. The usual term the standard model using Westervelt pressure formulation is of form ppt. However, this should be considered low-order approximation to more complex physical where higher order terms will required. Here we assume general case taken f(p) pt f unknown must recovered from data measurements. Corresponding typical measurement setup, overposed consist time trace observations acoustic at single point or on one-dimensional set Σ representing receiving transducer array fixed time. Additionally analysis well-posedness resulting pde, show injectivity linearized forward map use motivation several iterative schemes recover f. Numerical simulations also shown illustrate efficiency methods.