  We consider an undetermined coefficient inverse problem for a non-\\linear
partial differential equation occurring in high intensity ultrasound
propagation as used in acoustic tomography. In particular, we investigate the
recovery of the nonlinearity coefficient commonly labeled as $B/A$ in the
literature which is part of a space dependent coefficient $\kappa$ in the
Westervelt equation governing nonlinear acoustics. Corresponding to the typical
measurement setup, the overposed data consists of time trace measurements on
some zero or one dimensional set $\Sigma$ representing the receiving transducer
array. After an analysis of the map from $\kappa$ to the overposed data, we
show injectivity of its linearisation and use this as motivation for several
iterative schemes to recover $\kappa$. Numerical simulations will also be shown
to illustrate the efficiency of the methods.
